Golf is a game of tasks. Prepare for a tournament by knowing what tasks to assign yourself. Here is what I'm working on.
Knowing the pace of your greens is one of the best things you can do to practice for a tournament. This will arm you with an advantage for not just putting, but chipping as well.
Here, I'm using a couple of wedges to practice with. Knowing what shots you are going to use before they happen gives you a massive advantage in play.
As Phil Blackmar talked about, the mental game is everything. If you are concerned about your opponents, you might as well go home.