A book could be written on this subject. First thing is ask yourself what you want to accomplish. Do you want to shoot tournaments for fun or do you want to win? Since not everybody can win, you first need to have a good time. Strive to improve constantly and eventually you should be competitive. It will not happen overnight. When I shot tournaments, I shot in an indoor league twice a week. One 300 round on Thursdays and two on Mondays. I would also shoot at work during lunch breaks and at home in the evenings. I would shoot until my groups started getting bad due to fatigue, then concentrate even harder to shoot one great last group before quitting for the day. That's what worked for me anyway.
The hardest thing for a lot of people is trying to concentrate with so much going on around you. Most people practice by themselves so they are used to the "all alone" feeling when they are shooting. My best advice would be to put the blinders on, and concentrate on each shot. Most importantly...have fun with it. Good luck.
Also very good advise that JakeWym gave. Some tournaments are louder than others and all the people and noise can effect your shooting. If you can, try wearing a set of headphones and listen to your favorite music while shooting. It works good for a lot of shooters.
As for shooting, good form simply can't be stressed enough. Rock solid anchor, consistent foot placement and stance, follow through etc. All this must be done the same time after time, and practice, practice, and more practice is the only way to accomplish it.
As for gear, it goes without saying that the bow must be properly tuned and the arrows matched to it. Although a slightly heavier arrow can be more forgiving. A heavy poundage bow will only wear you out shooting a tournament, shoot a light weight bow, 40 to 50 lbs is more than enough. Speed isn't necessary for killing paper. Have a spare rest and release or tab if shooting fingers, that you've shot before with you. They can fail at very inappropriate times.
Good luck and let us know how it works out for you.