On foot
The island can be covered on foot, but there's not much to see on the slogs between the dock, the village and the beaches about 1 km each and it can be pretty sweaty work in the summer when there is no shade.
If you want to tour the island on foot, ask for a map at the information stand in the ferry terminal. They lend English maps with a 6km/2hr "nature educational" route that covers all the highlights. Don't forget to return the map before boarding the ferry at the end of your tour.
By bike
Probably the best way to get around is on bicycle. Prices are standardized at a rather steep ¥300/1500 for one hour/full day, the bike rental companies hang out at the dock and will transfer you for free. The money conscious traveller may want to rent the bicycle in Ishigaki and take it in the ferry, though the gain is not much since the ferry fee is at least an additional ¥400 each way.
Motorbikes are also available: a 50cc bike costs ¥800/4000 for one hour/full day, while a 70cc bike is ¥1000/5000.