Focus on one thing during each part of the tryouts / practice. For example, when you are hitting, think only of finding the ball, seeing the ball, and envision the ball hitting the sweet spot on your bat. When fielding, get your eyes on the ball, count the number of hops it takes as it is coming to you, or try to see the spin of the stitches. When pitching, pick out a smaller target than simply the catcher's mitt --- try a spot on his mitt --- and think only of hitting that tiny spot. Whenever other thoughts come into your head, start breathing through your nostrils and into your belly, hold it a second, then exhale slowly through your nose. Think about the breath going through your nose and down into your stomach, then think again about your one focus point (the ball, the target, etc.).
Also, whenever you start feeling nervous, remember why you are out on the field. Remember that you love the game and you enjoy playing it. Think about the millions of people who can't be where you are at that moment, for whatever reason (too old, too young, too sick, handicapped, etc.). Remember that the worst thing that can happen is you don't make the team --- which may seem awful but in the grand scope of things isn't so terrible. For example, there are people who can't walk, people who have lost their limbs or their eyesight --- so your situation could be worse.
Replace bad thoughts with good thoughts. For example, instead of worrying about missing a ground ball, think about how much you enjoy fielding grounders. See yourself getting in a good, low position, with your hands out in front of your body, fielding the ball. Visualize the ball going into your mitt, your other hand snapping down on top of it, feel the laces turning in your fingers, then throwing a perfect chest-high strike to the first baseman.
Visualization is a good way to mentally prepare yourself ... the more you see yourself doing something successfully, the more comfortable you will feel when you actually do it.