Capri travel

I'm not even sure you can rent a car on Capri. Public transport will get you around.

There are ferries departing from Naples and Sorrento frequently throughout the day. Lots of different companies operate the ferries, so just show up at the ticket office and buy a ticket for the next departure. There's no monetary advantage to buying a round-trip ticket, and that just unduly increases the pressure to make your return ferry. When you're ready to leave Capri, just go to the port and buy a ticket for the next departure. I've never run into it, but I assume some of the later ferries might fill up in the summertime, so you might not want to gamble on taking the last ferry out on any given day.
Ciao,
Meredith

scott,

As the others have mentioned, there are daily boats from Naples, Sorrento and Positano to Capri. You'll arrive at Marina Grande and can take the Funicular to the town of Capri, which is just slightly above the harbour. Capri is fairly small, so you walking is the best method to get around.

If you want to visit Annacapri (the other town on the island), there is public transit but I can't remember the details.

Be sure you confirm what time the last boat departs in the afternoon, as Capri Hotels will be expensive! I'd suggest buying a return ticket, as the harbour can be a bit busy and chaotic. I like to have the return ticket arranged so that I don't waste any time.

One other tip to mention. In the late afternoon, the queues for the Funicular down to the harbour can be long. If you think you might miss your boat, take one of the open-top Taxis back to the harbour (it's a nice drive).

Cheers!

I can concur with Ken. Take the ferry/hydrofoil to Capri and be mindful of the last ferry out and yes, the line to the funicular is long in the late afternoon. Take one of the open air taxis (60 Euro) to tour the island. I don't believe you can rent a car there.

You'll have to decide which side of Capri you want to explore.

We did the Arch, Villa Jovis and Capri City. This took all day
and was on foot. Villa Jovis from Capri City is a major up hill trek.
There are little electric transports for the locals,
but we couldn't figure out how to use them and these were always full.

We're going to have to go back to see the
Grotto, Anacapri and Monte Solaro. A car would do you no better
than the taxi and bus systems on the other side of the Island.
Be prepared to be a little assertive getting on the Boat Back. They don't have defined lines and people mob the gang plank.
If you have any problems with Claustrophobia, you may want to avoid the Hydrofoil. It gave me the willies with its lack of exits, it just felt unsafe to me and I've been boating all my life.