Play it like a practice match
I was scared in my first tourney and fortunately played a very bad opponent. I got the win but that gave me the honor of playing the number 1 seed. I did not fare so well (6-2, 6-1). I was actually pleased wth that score but it was a beat down nevertheless.
After about 3 to 4 tournaments, I was no longer nervous and viewed all matches as practice matches. My results quickly improved. It took about 15 tournaments to win a tournament. It was not the deepest tournament field but it was a 4.5 tournament victory nevertheless.
I would have been wise to start a level down but after reading the NTRP descriptions, I believed I was a 4.5-5.0 when I was more like a very strong 3.5 to average 4.0.
The real secret is to hit the ball with your practice swings and not change a thing. I hear people say I am crazy but before I started playing with my practice games, I would merely win the warm-up and take a serious beat down in the match against a player I had far superior strokes. When I relaxed and played my match with my warm-up game, I started winning.
Now, many years later, my age, knees, back, shoulder, two ruptured achilles tendons, I am back to a 4.0ish player. I hit the ball better then, but I know this old broken down player would annihilate that player who played his first tournament many years ago.