You're going to want to find a trainer or coach in your area and take a few lessons first. It's a fun sport and an easy one to get into..but you don't want to get into it on the wrong foot. It's very easy to just think "Oh I just run around three barrels..Pssh..Easy!" and that's just not the case.. You have to ease yourself and your horse into it at a speed that is right for you both, it's not something you can just quickly pick up.. With a trainer/coach though you should both be able to figure it out and slowly get better at it. Set small goals for yourself and your horse..It's nice to have that big goal out there but sometimes people can get discouraged when they are just looking at that big goal and it's not happening, look for those "big" small moments that are really big steps in themselves..
I started a great thread that most of the barrel racers have added even more good information and ideas to that you could check out and just read through, it will give you an idea of some of the things you're looking at, and even a ton of beginner things you can start to do with your horse.. Barrel Racing Exercises and Drills.
Just remember small goals, keep things slow, and just have fun with it! Good Luck!!