This question comes up from time to time here in this forum. I think I can answer for most of the experienced astrologers here when I suggest taking a class.
Whether you are wanting to understand how to cast a chart (doing the math longhand instead of getting a computer generated chart) OR wanting to learn how to understand and interpret a chart, BOTH require study and are outside the parameters of this forum, imo. It's just too lengthy a process. It would be like asking a group of biologists to teach you a course in this forum.
There has been a lot of information shared here which would be helpful to those with at least a basic understanding of astrology and there are a few who have started threads that provide some of those basics, but if you REALLY want to learn you must find a teacher locally and put in the time. Sorry, no shortcuts or shorthand ways to learn it. There are some online 'schools' in astrology too, if you are the type who can self educate without the need for a lot of back and forth dialogue.
Otherwise, I'd recommend either going to a "new age" bookstore and asking if they know of any classes on the subject, or call some astrologers and ask if they or someone they know is teaching a class.
When I was first starting out, my stepmother, who was an astrologer, cast my chart for me and gave me a few basics which piqued my interest enough to want to know more. I tried to get her to simply TELL me more about my chart, but she wisely directed me to learn on my own, and she would act as a supporting influence only.
So I signed up for a class locally and really enjoyed it. I learned so much about astrology and in the process about myself (through my chart).
I'm sure the astologers here would be happy to be a supporting influence and answer questions that may come up as you learn.
How much do you already know about astrology?
Here's a thread that was started here, covering the basics:
http://www.democraticunderground.com/discuss/duboard.php?az=show_mesg&forum=245&topic_id=5205&mesg_id=5205