The basic concepts of Astrology needs self study on your part and hence here we will assume that you are well equipped with the basics and proceed with this assumption. There being 12 Zodiac Signs and 12 Houses is an accepted and undisputed assumption all over the World.

In the Vedic context 27 Stars or Nakshatra's or Constellations are also being considered to be assigned in association with the 12 Signs and Houses. There are numerous methods of dividing 360 degrees into 12 parts or houses to which the 12 Signs  & 27 Stars are assigned. Each Star thus gets 13d-20m out of the 360 degrees. In any house or Sign a part of the Star spills over into the next house or Sign as per the calculations involved.

In simple terms each house is allocated 2-1/4 stars. Thus when a Planet is said to be placed in a house it shall be placed in one of the Stars as per its current location in degrees. This is still a part of the Vedic concept. The variable factor in Vedic concept was only the Planet visiting a House and moving into the 3 Stars allocated to the house. The House or Sign Lord and the 3 Star-Lords were fixed due to equal house concepts.
KP Basics
Ruling Planet's elaborated: The Sub lord is the deciding factor in all cases and KP attaches importance to the Sub Lords of different CUSPS and their Star deposit. In the analysis of any chart the CUSPS exclusively indicates the matters of that house alone. After assessing the matter, the time of fructification of such matters has to be found out and this led to the invention of the Ruling Planets.

The Ruling Planets are  Lord of the Day Lord of the Sign where moon is placed Lord of the Star where Moon is placed. Lord of the Lagna rising at the time of query. Lord of the Star where Lagna degree is formed. Nodes tenanting the signs of Ruling planets. These Ruling planets act as the guides and assist in timing the event almost exactly.

When applied to the Natal Chart, the Ruling Planets will agree fully with the dasha / Bhukti / Antar Dasha periods in operation. The Ruling Planets at the moment of Consultation agree with the Ruling Planets at the birth time or their Dasha and Bhukti's.

The Ruling Planets are selected in the order of strength, the Lagna Star Lord being the strongest. RP's are used to fix the date of realization of an event under consideration without resorting to the Horoscope or Horary, but using that particular moment of time to calculate these RP's.

The Sensitive degree formed or arrived by using Ruling Planets, when transited by the lagna degree, the exact hour and minute of the event can be told. If moon is moved to that sensitive degree the day of the event can be arrived at. If the Sun, then Month. If Jupiter then the Year can be arrived at.

The Order of selection of Ruling Planets is Star Lord of the Ascendant, Lord of the Ascendant, Star lord of the Nakshatra, Lord of the Rashi and then the Lord of the Day. Even though RP's are selected as in item (1) above, If a RP were to be in the Sub of another who is detrimental to the houses to be judged for a particular matter by being the significator of houses 8 and 12 to the house to be judged then this will not be a fruitful ruling planet.

If RP selected according to item (1), were to be in the Sub of a Retrograde planet then also this Ruling Planet is not useful. Hence while selecting Ruling planets these conditions are to be observed.

A Ruling Planet fails to offer results only when it is in a Sub of the Lord which is retrograde. If Rahu / Ketu were to be in conjunction with another Planet or aspected by another planet or if it were to be in a Sign without the above conditions then Rahu / Ketu will act as agents for the planets.

If inclined you are requested to read the 6 volumes published by Shri K. S. Krishnamurthi, regularly as a frequent review is necessary to understand and remember the basics of the subject.

The basics described here is only to create a background so as to support event analysis along with event tracking on a daily basis which is the main objective of this explanation. The proposed usage is not a defined or implied part of KP System.
Deviations from Vedic concept
The deviation from Vedic concept begins when equal houses are not considered and instead the Placidus system of house division has been adopted where each cusp i.e.. the beginning of a house has some unique measure in degrees - minutes unlike the Vedic concept where the cusp starts at 0 and ends at 30 degrees.

The Cusp of the House is considered to be a very important factor over the life time. The span of a house could be less than 30 degrees and hence the Sign associated with the Cusp will be limited to the span of the house and at times a sign may be completely missing or 2 houses may have the same signs. The House or the Cusp Lords will be as per the signs calculated by the Placidus system. This is one of the deviation from the Vedic concept.
Sub-division of Sign and Star
A planet  while moving in a span of a house will travel through the allocated stars, since a sign is divided into 2-1/4 star each star, represents a major division in a sign. In the adjacent figure the point E implies the eastern horizon and Aries Sign is shown co-incident. The first star is of Ketu and is shown in grey color followed by Venus, Sun, Moon, Mars, Rahu, Jupiter, Saturn and Mercury which covers 4 signs and is repeated 3 times to cover 12 signs of the zodiac. Each star is thus repeated at 120 degrees.

We thus have a total of 27 divisions in 360 degrees each segment being 13d-20m. This is only a rough measure. Imagine that you have some length of a stick  which you would like to use as a measuring tool. You may sub-divide this stick by any means into finite sections, may be equal or unequal depending on your end use. The time when you decide to use this as a tool you discover that some objects are falling between the markings, you then realize the need to sub-divide to come to a finer measure.

This conclusion was also arrived at by the propounder of KP System and he sub-divided the span of each star into smaller portions called as a Sub-division or a Sub. This Sub when further divided into finer sections is called as a Sub-Sub which will be referred to as SSL, The next will be SS4 followed by SS5, SS6.
We are all aware that a measuring tool would also need some Units of measure then its sub-units followed by a sub-sub part of it. The unit of measure adopted by KP is the Vimshottari Mahadasha Paddhati again an accepted Vedic concept based on the 7 Planets and 2 Nodes, each planet being allocated a fixed number of years. The span of each Star is divided into 9 parts in accordance with Vimshottari Mahadasha Paddhati as the primary Sub  division, again he has sub-divided each primary Sub division or 1/9th part into 9 parts which are called as Sub-Sub. This is a very important contributing factor for the accuracy of predictions as the resolution or the least count has now increased.

A transiting planet is a variable, next is the Sign-Lord followed by Star-Lord. This transiting planet will now occupy one of the 9 Sub-parts in the Star, this sub-part is ruled by one of the 9 planets hence the term Sub-Lord was introduced followed by the Sub-Sub-Lord. The planet transiting a house is now a source of an event, Star-Lord, Sub-Lord, Sub-Sub-Lord and the Sign-Lord will decide the course of events indicated by the House.

This is only a preliminary explanation for one planet whereas there are other such 8 entities which will contribute and offer variations to the event as projected by the house. We have earlier discussed that the Placidus system of house division results in each cusp having some unique measure in degrees - minutes.

These 12 Cusp's are given the same consideration as given to the planets explained in the above paragraph. Thus each Cusp has a Star-Lord, Sub-Lord and the Cusp-Lord which is the Sign-Lord himself. These stay fixed throughout the lifetime in a Natal Chart. Refinement to Vedic Astrology as you must have now realized is due to the introduction of additional variables for the Cusps & Planets.

The nature / type of event for each house depends on the Lords of star, sub & sign on the cusp. Planet is a source of event having a star, sub & sign lords. A sub-sub is considered at times to improve the precision.

The relationship between all the above variables and the additional parameters which are partly derived from the Vedic concept and partly from the Western concepts are called as the Rules of KP or Krishnamurti Paddhati itself.

KP has recommended the use of Ayanamsa which varies for each year. This Ayanamsa is closer to Chitrapaksh. Chitrapaksh or Lahiri Ayanamsa differs with KP Ayanamsa by 6M. The yearly rate of change assumed in KP is 50.2388475 Seconds.
Every planet in its Dasha, Bhukti and the house it occupies does not give results for occupied house but gives results according to the house where the Star-Lord is placed. Planet 'A' offers the result of the house occupied by the Lord of Star 'B', wherein this planet 'A' is deposited. Results being Good or Bad is decided by the Lord of Dasha and Bhukti being placed in the Sub portion of which Planet.

Rahu - Ketu i.e. Moons North Node ( MNN ) - South Node ( MSN ) the shadow planets are very important and they do not have a specific Sign assigned to them. The Signs associated with the Planets are not important as the Nakshatra Swami ( Star-Lord ) is more important. Any planet when it is placed in a Nakshatra has more power than the Lord of Nakshatra.

In a natal horoscope if any planet is Retrograde then it does no harm and is to be considered as in normal motion. In Prashna Kundali a retrograde planet gives results only in direct motion, retrograde planet is considered powerless.

KP assumes that no Planet is Good or Bad by itself. In KP all Western Style Aspects ( Graha -Yog ) are accepted along with all Indian Style Drishti-Yog.

Working Rules of KP System For each Planet consider in which Star it is placed. The Star-Lord of this planet owns a house or houses and will indicate the event matters of those houses owned by the Star-Lord.

The Planet will occupy a Sub portion, the Sub-Lord of the Planet also owns a house or houses. The nature of house decides if the event indicated by the Star-Lord is good or Bad. Planet considered to be a Benefic by Lordship offers the results signified by it, through the Planet deposited in its Stars. Planet is the source, star-lord shows the nature of results and Sub-Lord decides whether the event is favorable or not.
The Order of Giving results will take place during the Dasha / Bhukti. Significators when are favorably aspected / conjoined in favorable houses with outer planets by Drishti / degrees act as significators.

Mars, Saturn and Jupiter influence the inner planets Venus Moon Mercury. Except Rahu-Ketu all others assist in Trine aspect and offer its house results and help the occupant i.e.. the aspected significator. Likewise Evil Aspects also hinder the event.

Rahu and Ketu are exceptions as they completely replace the Planets conjoined with it or aspecting it in any manner. Dasha / Bhukti / Anthra brings an event matter to happen very close to the timing of the event. They will handover the matter to Sun, Moon and the current Lagna for completion.

How to use the KP System KP has classified the relationship of Questions with the houses and its groups. A definite sequence exists to evaluate the strength of planets. This is indicated by the Ruling Planets at the time the question is asked. Planets indicate the ways and means of the results based on its location in the respective houses.

The Star-Lord indicates the subjective results and the Sub-Lord indicates whether the event will take place or not.
The timing of any event depends upon Gochar Bhraman ( Transit ) of Sun - Moon, Lords of Dasha, Bhukti and Anthra. A Planet tenanting a Star affects the matters of the house occupied by the Star Lord and also the houses owned by the Planet.

The Occupant of the house will move the matter of the house it occupies, apart from the results it has to offer due to its star position if there is no planet in any of its 3 Stars. Whether or not such results as are indicated by the tenant planet will come to pass depends on the Sub portion of the Star occupied by the tenant planet.

If the Lord of the SUB occupied by the tenant planet is favorable connected by Occupation, Lordship to the matters signified by the Star Lord of the tenant Planet, the tenant Planet fructifies the matter of which it is the significator due to its Star position.

If the tenant planet is placed in the SUB of a planet who occupies or owns houses detrimental to the affairs of the Star Lord, the matter is not fulfilled. The Sub Lord should not be in unfavorable aspect to the CUSP of the house signified by the Star Lord.

The aspects are to be computed by reckoning the distance in terms of longitudes. Star Lord compares with Dasha Lord, Sub Lord with Bhukti and Anthra to Sub Sub-Lord.

Planet becomes a Malefic / Benefic by reason of its owning or occupying Benefic / Malefic houses. If a planet has to offer the results of its own house or houses in full measure, first it should not be under the control of another planet. In short no planet should be in any one of the 3 stars of the said planet.

Any planet be it for any lagna, if it has to offer the results of the house it occupies and the house it owns, then it must be deposited in any one of its own 3 stars and in its own Subdivision out of the 9 Subdivisions. Then only the said planet will come into the picture to offer the results in full measure depending on how it is conditioned by its own sub, which has the say, favorable or unfavorable, advantageous or disadvantageous, Yes or No.
Ruling Planets are the Key to Timings In KP the Ruling Planets at the time of the question are the same at the time of Results.

Lord of the Ascendant Sign In the current place and time.
Star-Lord of the Nakshatra where Moon is placed.
Rashi-Lord (Sign Lord) of the Sign (Rashi) in which Moon is placed.
Day Ruler for the day under consideration.

These 4 Planets are Ruling Planets.
Nak-Lords and Sub-Lords of Ruling Planets should be ignored only when Ruling Planets are to be considered.

Neglect those that are retrograde from these 4 planets. If the retrograde planets are forming or are in any aspect in degrees then they can be considered as part of Ruling Planet Group. If along with the 4 planets MNN-Rahu or MSN-Ketu are in the same sign as the planets then Rahu and Ketu are added to the Ruling Planet Group and are Important.

In the Ruling Planets Group the Lord of the Ascendant is more important as he changes only after 2 hrs. Next important planet is the Star-Lord of the Nakshatra in which Moon is placed. If out of 4 planets if only 1 is retrograde then it can be considered for inclusion in the group. This retrograde planet gives results only when it crosses its degrees at the point it goes in direct motion. This helps in deciding matters pertaining to events to occur after a few days. For that specific day they are to be ignored.

The Day ruler is to be considered from one Sunset to another only and should not be changed at midnight as a day is considered from one Sunset to another sunset.

In special circumstances consider the specific degrees of the ascendant and if these degrees indicate that the Lord of the Star is not the same as the lord of ascendant then the Star-Lord corresponding to the degrees is to be considered as the Lord of the ascendant. This needs to be used only on rare occasions only.
Events in 24 hrs: by checking the Movements of the Ascendant amongst the Ruling Planets. Events in few hrs or short time : Consider the Ascendant.
Events in a month: Moons Movement amongst the Ruling Planets. The day moon goes into the Star of the Ruling planet the event will take place.
Events after a month: Events related to Employment, time of Child Birth, Starting of Closed Industries, Allotment of House when on a Waiting List. Consider the Movements of Sun, this will decide the month and movements of Moon will decide the day.
Events which need a year or more: Consider the Movement of Jupiter or Dasha, Bhukti and Anthra.

In KP each planet has a Sub-Lord whose effects are most prominently seen in predictions. If in one Nakshatra 2 planets are present and if the Sub-Lords are different for each then different results are experienced.

In KP the Planets may be in any house and if the Star-Lord of that house is in a positive or auspicious house then all the planets in that house will give beneficial results. In KP any planet if it is related to a house then the results are decided by the house under consideration.

In KP the Star-Lord gives results as per the Houses whereas Good or Bad is decided by the Sub-Lord.