It takes anywhere from 6 months to 2 years to fully train a barrel racing horse. Therefore, ClaPort already mentioned, your horse should have a solid foundation on general riding before you do any barrel work. I would also add to that list:
-be able to do simple lead changes (even better if you can also do flying lead changes)
-can make perfect circles with one hand (which means neck reining)
-vertical and horizontal flexion including breaking at the poll
-can control every part of your horses body including head, neck, shoulder, and hindquarters.
I myself have been running barrels since I was a little kid, and you never stop learning and never know it all. I just purchased Dena Kirkpatricks barrel racing DVD and I watched the whole thing this weekend. It was awesome! Along with getting a trainer, I highly recommend getting your hands on any books of DVDs regarding training. You can start on YouTube as Dena does have a bunch of free videos. Here's one of hers that will take you to others if you click on her channel.
And for reference, I started my current horse Red on the barrels at the end of June/beginning of July, and we have JUST started to gallop the pattern almost 2 months later. SLOW SLOW SLOW is the key to getting a fast, good, correct, barrel horse.