Once you arrive in Ischia off the boat, you will have no trouble getting around. There is a small bus system that loops around the island continuously. It cost 1,20 euro for a 90 minute ticket which you validate on the bus. It would seem that residents, especially old and school age, do not need tickets but you as a tourist do. It is a good and easy way to navigate the island. Our hotel sold tickets, newstands and tobbaco shops sold tickets.
We decided to rent a moke for about 30 Euros per day on a whim. Let me tell you, the experience in itself was worth so much more! It's hard to take yourself seriously as you drive around in one of these vehicles... Trust me! If you don't believe me, ask me to tell you the story about the bus stop or the dead end next to the block of apartments.
I guess you have the choice of ferry or hydrofoil to Ischia from Naples. We chose the hydrofoil as it takes 1/2 the time at 45 minutes. Plus it was great fun. The one way trip from Naples to Ischia was 11,50 euro. From the naples train station, the bus station is right next door, take the bus to Beverello porta (about 10 minutes) and at the docks there are signs pointing you in the right directions for where you need to go.