Get tickets and join the crowds at a game at Damaschke Field. If there's nothing on while you're there, you might like to check if they give a guided tour of the grounds.
You'll be spoiled for sightseeing choice when visiting Oneonta. Damaschke Field is an ideal place to begin here, but there are plenty of other worthy sights to explore. Cooperstown All Star Village Fields, State University of New York-Oneonta, and Hartwick College are near the sporting facility and will round out your day nicely.