what is the process of if someone was hitting a ball, and then watching the ball, and finally catching a ball.

Do you want both sensory and motor processes? Are these three distinct acts or just part of a series of behavioral acts (e.g., catching your own foul ball)?

You have the visual processes keeping track of the ball and the muscle movements of swinging the bat and catching it, sensing the bat and the glove, along with the feedback from the muscles.

How detailed do you want to be?

I hope this helps. If not, repost with more specifics.