BR86 did a great job explaining this. If you want in depth information on barrels, there are many books and DVDs you could look into that cover training and competition. There is also a lot of information available on the internet, but I prefer the books (because their authors have more credibility and the books are more in depth). If you are a visual learner, look into the videos.
Another option for you might be attending a clinic. I've done that, and I learned a lot from the clinicians as well as the other participants. However, unless the clinic is for starting barrel horses, you'd want to get the basics on them first to get the most out of it.
I just looked at the books currently available, and found the one by Ed and Martha Wright. I was so excited, I just had to order it. (They put on the clinic I attended.) But I would look for authors whose names you've probably heard - Sharon Camarillo, Marlene McRae (sp?), Charmayne James, etc. If you find a book written by someone you've never heard of, do a little research to find out what his/her credentials are. I've seen a lot of stuff (mostly on the internet) that really made me scratch my head until I discovered that the author had never run a barrel pattern before. There is also at least one book on gymkhana and a pole bending video.
Just an interesting side note, I ride appaloosas, and when the arena is big enough at our breed shows, we run horse against horse, which is tons of fun. We only do it for barrels and poles, but, wow!
Learning never stops