Two things to start with before you get to any of the practical details people have mentioned here.
1. Decide what kind of flying you want to do and what kind of aircraft meet that need. The original poster said something aerobatic, which helps define the need, but even at that there is a lot of variety. Single or two-seater? High or low wing, or biplane? Competing seriously or just going to have a bit of fun? Pitts, Skybolt, Decathalon, Cap 10?
2. Join a group for the people before the aircraft. A nice aircraft with a group of jerks around it will result in a miserable experience. How they treat each other is as important (some would argue MORE important) than how they treat the airplane.
After that you get into the practical things like location of the aircraft, rules to give everyone a fair shot at availability, quality and timeliness of the maintenance and the other good points which have been made here. Take some time to let yourself be known in the community and let people know that you're looking. Shares can often become available if the right person is looking.
Good luck!
Pitts2112