The most important thing to do while playing center field in fastpitch softball is to position yourself according to the batter. If the batter is a hard-hitter, then it is most suitable to stay back. On the other hand, if the batter is somewhat small and is not capable of hitting the ball too far, then it is best to move in. Sometimes, you must take the situation in mind while positioning yourself. If you want to prevent a big play such as bases-clearing double, then you should move back and if there is nobody on the bases, then simply stand where you think the batter is most likely to hit.
Make sure you have a clear view of the batter so that you can immediately see him/her making contact with the ball and knowing the direction in which the ball has been hit. If it has been hit in your direction, detecting it early will allow yourself to react to it more quickly. Do keep in mind that instead of moving in as soon as the ball has been hit, stay back. Running backwards is harder as compared to moving in.
If there is a high fly ball, you will naturally need to move fast to get under it. Instead of running on your heels, run on your toes, as that would allow you to cover the ground quickly without losing sight of the ball. Running on heels would cause you to slightly hop, which will make it harder to see the ball clearly and judge it properly.
When there is a runner on first base, it is your responsibility to keep an eye on them and keep them from stealing second base.
Always throw the ball to the cut-off man at a height of about two feet over their head. This will allow them to cut if off and throw it to another base, or let it through if necessary.