It depends on how far you want to take it. If you're planning to compete then getting an experienced trainer would be no.1 priority. But for fun, I'd say a mix of asking experienced barrel racers, watching youtube vids and this forum could do it for ya.
The main thing is to start out nice and slow, you won't be running the pattern for quite a while. Circles and figure eights are your friends, work on prompt movement and flexions off your legs and other rein aids, and just have fun with it, keep your balance in check, try not to lean heavily this way and that in the saddle as it is one more thing your horse has to be accountable for getting around the course.
Most important part is to have fun with it! Good luck!
Welcome to the forums! Barrel racing is a blast for us speed demons. ;-)
The BEST advice I can give you is to get a barrel racing trainer. You can't learn to fly a plane online, can you? Why should learning an event with a horse be any different? You can't learn barrel racing online.
Sure, you can putz around on the barrels and do things just for fun. But even if you can take a couple lessons from a barrel racing trainer, it will help you progress more quickly than if you tried to do it on your own via trial-and-error. Why make mistakes when you can learn from someone who has been there and done that, and can help you avoid those mistakes?
The key thing with training a horse for barrels is SLOW. If you go too fast too soon, you create bad habits on the barrel pattern that can be very difficult to fix. Or you could sour and ruin your horse on the barrels if you go faster than they are ready for, and frustrate them. So SLOW is the name of the game when you are learning.
Your horse should be 100% broke before you start barrel racing training. You should be able to control every piece of your horse's body: head, neck, shoulders, ribcage, and hips. You need total body control to get through the pattern correctly and quickly.
Just starting out, you don't have to have any fancy equipment or tack. But if you do choose to get more serious about it, then a barrel racing saddle would be a wise investment. I'm a strong advocate for protective sport boots, because they are cheap insurance against knicks and scrapes and bigger things.