|My birth chart, generated with OpenAstro.org|
The most important thing to remember, when you read a chart, is that the process is equal parts analysis and synthesis. That is, you can't simply look at each individual planet and sign (and degree) and drill into it and explain it in isolation with the expectation that you'll thus develop a coherent narrative. The process of reading a chart is much more like looking at a picture than reading a book. That is, you have to pay attention to the whole, and while you can take in the details, they are meaningless without their relationships.
For example, my Sun is in Cancer, in my fourth house. While certainly that says a lot about me, it would be foolish to ignore that my Sun is also opposed to my Neptune, or trine my Moon and Ascendant, or conjunct my Mars. All of those things - regardless of their meaning - influence the essential core of "Sun in Cancer, 4th house." Indeed, they influence it so much that two people with the same planet in the same sign and same house might have completely different manifestations of that aspect based upon the other planets in the chart.
Before we get into individual planets and signs, then, the first thing I do when reading a chart is look at overall shape. Are the planets clustered or spread apart? Are they mostly on the top, or on the bottom? Are there any planets sitting out by themselves, or are there groups of several in the same place?
As you can see, my chart is dominated by a set of planets on the bottom - in the 2nd through 5th houses - and another set on the top, in the 8th through 10th. Jupiter - indicated by the symbol that looks like a 4 - is alone in my 12th house, the only planet not clustered around either of those areas.
What does this shape mean? Well, I don't show a strong East-West (Left-Right; opposite from a map, because we're looking at the sky) bias, or a strong North-South (Bottom-Top) tendency. Usually, someone who's strong on the Eastern part of the chart is self-defined and self-directed, more likely to try to change a situation to match his or her needs, whereas someone strong in the Western part of the chart is more likely to "go with the flow" and adapt him or herself to whatever circumstances arise. The presence of my Jupiter in the 12th suggests at least some Eastern influence in my chart, but, really, I'm not pulled strongly either way. Indeed, that I have almost no planets in either direction means the question of self-defined versus circumstances-defined is something that I don't really even process. I'm more liable to say that I am both, and/or neither, that the dichotomy there is only a seeming one, which in reality isn't a dichotomy at all. Sounds like me, no?
As for the top and bottom of the chart, I likewise don't have a particular tendency here, but rather than having no planets to the North (bottom) or South (top), all of my planets go one way or the other. I would say that, were the East-West question is almost a non-issue to me, the question of whether I am an internal, introverted person or an external, social person is a profoundly difficult one for me to answer. That is, while I have undeniably strong introverted tendencies - my Sun is bellow the horizon, along with my Mars, my Mercury, and my Venus - I am also more than capable of talking to people and, sometimes, talking their ears off. I can be a public speaker, and am more than happy to show off many of my eccentricities to the world (signified, particularly, by my Uranus - the one that looks like a capital H with a line through it - on my "midheaven").
Here, again, I might say that the seeming dichotomy between the two isn't really a dichotomy at all, but for a completely different reason. Where I don't feel as though either self-definition or circumstantial-definition really applies to me, I feel all-too-much that both introversion and extroversion do apply to me, just in different ways at different times.
Having considered the shape of the chart, the next step I usually take - especially when using OpenAstro, which calculates it for me - is to look at elemental influences. The chart is composed, fundamentally, of only seven different types of energies. That is, there are 4 elements and 3 modalities that basically explain every sign, planet, and house. "Huh?" you ask? "There are 12 houses, 12 signs, and 10 planets (or 12, if you count Chairon and the node, which I leave in). What are you talking about?" Let me explain.
There are four elements in astrology, the classical elements of the ancient Greeks: fire, water, air, and earth. There are also three modalities: cardinal, fixed, and mutable. Now, four elements times three modalities equals twelve signs. Or, in other words, each sign has an element (you've probably heard that Leo is a fire sign, for example), and each element has three signs, one for each modality. So, for example, Leo, Sagittarius, and Aries are the three fire signs. Aries is cardinal, Leo is fixed, and Sagittarius is mutable.
Usually, when you're learning astrology, whatever book you're looking at will ask you to memorize the dates and qualities of each sign, as if they are all unique. That's a fair thing to do, but it misses the mythological and elemental core of the practice. If you learn, instead, the meanings of the elements, and the meanings of the modalities, you can synthesize them to figure out what any given sign means. For example, Leo is a fixed sign, and a fire sign. That means it has fixed energy: it is focus, determined, sometimes stubborn and lazy, devoted, and other stationary type adjectives. It is also a fire sign, meaning it is passionate, intense, loud, and generally fiery. Compare that to a Sagittarius, who is just as passionate and intense, but is mutable, and therefore has flighty, changeable, wandering energy instead of stubborn or lazy energy. Voila, without memorizing the qualities of Leo or Sagittarius, you've generated explanations of both signs out of their elements.
My bias, then, is always to push towards elements and modalities. There are dozens of influences in the chart, some extremely subtle, and for exactly that reason - because the thing is so freaking complicated - it's vital to try to break it down into fundamental building blocks that can be put together to form a coherent narrative.
In my chart, as OpenAstro tells you at the upper left (calculating based upon which signs my planets are in, giving more weight to more important planets), there's a lot of water energy, and not so much air or fire. There's also a fair amount of earth. What this means, in broad strokes, is that I am an emotional person. I feel things strongly, and am naturally empathetic (to the point of sometimes over-estimating the emotions of others). This much water does not mean that I am innately sensitive - though at times I can be very sensitive - because it can also indicate that I am emotionally very strong as well. In short, I have a deep emotional well, which can manifest itself as strength or weakness depending upon the situation.
Water is not merely emotion and empathy, however. It also indicates spirituality and mysticism, and is linked with artistic practice (if not always inspiration, which is more of a fire-sign tendency). I would submit that my interest in astrology and my particular way of reading charts - which tries to break down people's personalities to their emotional, psychological, and spiritual essences - is emblematic of a person strong in water.
Air is the sign of intellect, and while I consider myself an intellectual and an academic, it is not strong in my chart. That, however, does not mean that I am not intelligent; rather, it means that my thinking is not as rigorous or calculated as a pure air-sign native's would be. I can be focused and calculating - my earth influences do help me stick to tasks, including intellectual ones - but my intellectual decisions are largely decided based upon emotional, psychological, or spiritual concerns, and not purely academic ones.
Having taken in hemispheres and elements, I might also take a look at modalities. My own modalities are balanced between cardinal, mutable, and fixed, but some people show a preponderance or absence of one. A pure mutable person, for example, is usually an extreme perfectionist and procrastinator, unwilling to ever be finished with something, and yet, at the same time, very easy going and not worried about getting things done. A cardinal person will jump from idea to idea, never finishing anything, but always inspiring either him or herself or others to take on some new project. A fixed person may be difficult to get moving sometimes, but will often fear change, and will establish routines, and will finish and start things on time.
Obviously, all three modalities are useful in different circumstances, and potentially dangerous in others. Sometimes the initiator needs to finish things, sometimes the perfectionist needs to meet deadlines, and sometimes the diligent, trusty worker needs to shake up the routine to stay sane. That's why it's so important to remember that charts do not only contain within them myriad interactions between planets and signs, but also that the world itself and the other people in it effect our charts in profound ways. If I am "missing" a planet that might give me a favorable aspect, and I meet someone who has that planet, it might just let me accomplish things I couldn't accomplish on my own.
Believe it or not, my first time sitting down with a chart, this is all I look at. Oh, I'll glance at where the Sun, Moon, and Ascendant are, and I might notice particularly prevalent aspects (I have a grand trine and a t-cross in my chart, for example). But the fundamental first steps to reading a chart are much like the fundamental first steps to engaging with a painting, or a musical piece. First you step back, take it all in, and look or listen for basic things like style and structure. Analyzing harmonies, deciding which aspect influences career success, (or which light source is casting that shadow, or which subdominant substitution is used when) comes later.
I suppose I'm trying to form a question, in these last two posts: what is astrology? Is it an art, or is it a science, or is it a craft (a techne, in Greek)? I think it is all of those things. Then again, I also think that music is all of those things, and, what's more, listening to music is all of those things. What is so brilliant about astrology, however, is that the thousands of ways of interpreting a chart - the thousands of different processes, as well as outcomes, that make up the art/science/craft - are all contained within the practice itself. Astrology is meant to be different for different people, it's meant to be an exploration of interactions not just between elements or planets in a chart, but between people.
If you ever do work with an astrologer, I recommend this, that you see the experience as a dialogue. Astrologers are not mere mystics and entertainers trying to divine your past or future. They are like counselors, or close friends, who are also students of human nature and the universe, asking questions and seeking answers in a way that may seem unscientific, but is in fact purely and especially human. Engage in that dialogue, seek that wisdom, and see how your energies play off against someone who is an expert in engaging in that kind of conversation. After all, astrology is fundamentally about finding one's place in the universe, a task we can all agree is worthwhile.