There are several ways to explore Sun Moon Lake.
You could hop on the official tourism bus which circles the island, or rent a bicycle to explore the scenic surroundings. Or you could opt for boat rides.
If you're pressed for time, the boat ride is a good idea. Boats will reach the different piers in intervals of 20-30 minutes. I can't think of a suitable comparison, it's similar to island hopping. In this case, lake hopping.