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?
I would check out the sticky we made for beginners: Barrel Racing Exercises and Drills.
Lots of great information in that.
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.
Good luck and keep us posted.