Renting a motorcycle is the most practical option, and this will cost you about Rp 80,000-120,000. Look for vendors in Toyopakeh and Sampalan (or more likely, they will find you!). You may be able to find a rental vehicle but they are not common.
Some visitors from Nusa Lembongan arrive with rented pushbikes - make sure you get permission to take the bike off Nusa Lembongan first. You should note that roads in Nusa Penida are rough, hilly away from the north coast, and in remote areas no more than stone-strewn tracks.
Local public transport is in small old bemos or on the back of a truck. These vehicles ply the north coast road with some regularity, but elsewhere on the island do not bank on anything.