Right field is an important position that almost always tries to head off the runner at first base. You should be good at catching on the run and making long throws back to the diamond for plays at the bases.
Be in position when the ball is pitched, but be ready to move as the ball is hit.
Monitor fly balls and position yourself accordingly. You want to head for a point of interception and meet the ball. If you're running back, look at the ball instead of where you're going so you won't lose sight of it.
Keep running when you catch the ball and use that momentum for the throw. This will help you throw the ball farther.
Remember that fly balls are only a small part of your job. You'll also field base hits and be the first baseman's backup. Once you field the ball, throw to first immediately to cut the runner off. If she's already past first, cut her off at second.
Charge at ground balls with your hands out. If the ball is on the opposite side of your glove and you need to cross over to get it, pivot on the balls of your feet instead of bending in the middle - this will help you balance.
Throw the ball overhand, to keep it fast and low to the ground. Consider low, one-hop throws, as they save time and cover more distance.