In this post I intend to explain the most fundamental philosophy behind astrology the way I see it. I will avoid too much technical stuff and focus on the principles.
One of the most common misconception regarding astrology is that there are twelve star-signs; and around the year, for some arbitrary reason, people born at certain dates are assigned certain such signs. Then some goofy "astrologer" imagine the future events for each and everyone, and there are only twelve possible futures, which can be read in most newspapers. This has as much to do with astrology as phlogiston has to do with fire (none at all). Were you really convinced of newspapers telling the truth?
Another common misconception is that astrology is based on the idea that the stars are deciding our lives; this would be like saying that Tarot is about cards deciding our lives. The cards and the stars are a medium for randomness, and the idea is that through randomness we can communicate with the divine. Chaos is the basis of all divination, and it's possible to use any type of agent of chaos, such as: dice, coins, the flight of birds, the palm of the hand, or the shapes in tea-leaves. Incidentally, astrology and tarot makes use of exactly the same symbols, and also geomancy and cheiromancy; thus we could say that astrology is a language of symbols for describing and understanding the soul, which in extension is the essence of the divine.
So, when we try to explain astrology, we should not see it as the stars shaping the patterns of our lives, but instead as the basis of all divination: which is a means of communicating with the divine. Of course, the stars do not move randomly, in fact they scarcely move at all from the viewpoint of a human lifetime; it is actually the planets that make up the source of randomness and though they move in very ordered orbits which we can calculate thousands of years in either direction in time—when we place them in a chart they appear as random; in the same way that there is nothing truly random about mixing cards, they only appear mixed to our limited minds, excluding a few individuals with savant abilities.
Western astrology doesn't even make use of the actual stars in the sky, but instead an imaginary zodiac of how the sky looked about two thousand years ago; it is called the tropical zodiac. This should tell us how little astrology has to do with the stars, except for the Sun which in astrology is considered a planet because of its apparent (from our viewpoint) orbit around the earth. The planets are what we are looking at, and their positions from a physical point in space at a certain time is what we call a horoscope. It would be completely possible to make a horoscope for a person born on the planet Mars or Venus, but since there are no known actual subjects this is merely hypothetical.

Each planet is like an instrument in an orchestra, and the orchestra is playing the soundtrack of our lives. Whether we act on the music playing at a certain time is our choice to make, but the philosophy of astrology is that when a certain tune is playing it is favourable to act upon it; when Venus plays her love-tune, we might more easily fall in love, and when Mars plays his action-theme it is more fitting to be the action-hero. We are not compelled or forced by the planets, it is more that they inspire us, like a full Moon.
It is not that the planets actually sound in any way, or that they radiate some mystical force; but some sensitive astrologers do actually feel the influence of the planets in a very real way, as intuition. If the planets do have any metaphysical radiation is unknown and would only be wild speculation (but the Sun's radiation makes life possible and the Moon makes all the oceans ebb and flow with its gravity).
Astrology as a science is a very precise one, it is actually as precise as mathematics and one of very few sciences that can be as precise as that. It is important though to differentiate between astrology as a language and astrology as an art of divination; the latter is the application of the science and as with mathematics it may be flawed or misinterpreted, e.g. 1+1=3 is generally considered flawed mathematics or a misinterpretation of how to apply it (the way mathematics at present time is understood). A birth chart is only as exact as the astronomical calculations we have to position the planets, and though the definitions of all the symbols in the chart are absolutely exact, the understanding of them and how to interpret them is an art-form rather than science. So when someone claims that astrology is a science, they would be completely correct unless they also include the divination and interpretation in their definition.
The zodiac is logically structured in such a way that the four classical elements rotate in the following order: fire, earth, air and water. In the same manner there are three qualities: cardinal, fixed and mutable. Thus we get: Aires (cardinal fire), Taurus (fixed earth), Gemini (mutable air), Cancer (cardinal water), Leo (fixed fire), Virgo (mutable earth), Libra (cardinal air), Scorpio (fixed water), Sagittarius (mutable fire), Capricorn (cardinal earth), Aquarius (fixed air), Pisces (mutable water). As you can see it results in all possible combinations.
In our orchestra each sign in the zodiac could be imagined as a specific melody or rhythm. So let's say that Venus plays the harp and Mars the drums; then imagine that fire-signs have an energetic and powerful theme, earth-signs a harmonious and calm theme, air is visionary and thought provoking, and water emotional and dreamy. It seems natural that Mars enjoy to play drums with an energetic and powerful rhythm, and so finds himself more at home with cardinal fire: the sign of Aires; and therefore it is said that Mars rules Aires. In the same way, Venus resonates in harmony while playing the beautiful melodies relating to Taurus, or the romantic and aesthetically pleasing themes associated with Libra, and so Venus is said to rule the signs Taurus and Libra. When planets are in the sign they rule, their sound becomes stronger and can be heard louder in relation to the other planets.
Planets relate to each other also, by looking at the difference in degrees on the chart between them; this is called aspects. The most common aspects can easily be found by looking at the chart and counting the number of signs they are apart, and the difference in degree in their respective sign should be as close to each other as possible, i.e. the closer the stronger the effect. Planets on the opposite side of the zodiac are in opposition; they are forcing the influence in opposite directions. Similarly planets in the same sign may or may not cooperate, if they do they strengthen each other, otherwise they compete for dominance; this is called conjunction. When planets are three signs apart, that is in a 90° angle, and of the same quality (but not the same or opposite sign), it is not considered a harmonious aspect; this is called a square. Planets four signs apart, that is in a 120° angle, and of the same element (but not same sign), this is thought of as the planets are working well together; this aspect is called trine. There are a few additional aspects, for more advanced studies.
Considering our orchestra again; planets with many favourable aspects would be thought of playing beautiful music, the instruments strengthen and flow naturally with each other. On the other hand, planets with many unfavourable aspects may not even be considered as playing music, and you might get a bit of a headache from listening to it.
This concludes the first post on Astrology Philosophy, but a follow-up will come later on.