Ferries and hydrofoils etc for the most part depart from the main port in Naples (Beverello).

There is a shuttle bus service from Naples Airport to the port via the main station (Napoli Centrale / Piazza Garibaldi). It departs from just outside the arrivals terminal and tickets can be bought from the driver, who will probably be the vaguely official-looking guy in sunglasses standing by the bus (!). I think it's 3 euros single. It only calls at the main station and the port - but when you get to the port it might not look like it, as the bus stop is actually the other side of a busy main road. Crossing this road is a bit of an art form - don't assume that the cars will stop at a red traffic light, and be particularly careful of the mopeds / scooters. If you watch the locals doing it, they basically just walk confidently out in front of the traffic. If you wait for someone to stop for you, you'll be there for hours. The best thing is often to walk close behind someone who looks local! If you prefer, you can take a taxi from the airport. Taxis in Naples have a list of fares between the most popular destinations, and the driver should show you this and ask if you want that fare. When I've done it, the driver has actually given me a bit of paper with a copy of the list of fares on it and marked the fare I'll be charged. A year ago I paid 16 euros (Beverello to the airport), so I wouldn't pay very much more than that. Be firm (and loud!) if at the end of the journey you're charged more than you agreed.

If you're at the entrance to the port with your back to the main road, you don't the big building directly in front of you - that's for longer haul ferries etc. To the right there's a departure board with boats to Ischia, Procida, Capri, etc and just down the side of that down a few steps are the various ticket offices. You don't need to have booked tickets in advance or even to have decided what boat you want to be on. They are run by a few different companies and are quite frequent. So basically just look at the board and see what the next departure is, then go to the appropriate ticket window. Be careful here, as sometimes there are some 'unsavoury' characters here, so don't be distracted when you're at the ticket window. Keep your ticket and show it when asked when you get on the boat. Incidentally, Forio is pronounced with the stress on the 'I' - fo-REE-o, Casamicciola with the stress on the 'mi' - casa-MI-chola.

Boat-wise, there are a few options:

Alilauro run fast hydrofoils ('aliscafi') to Ischia Porto and Forio

Caremar run hydrofoils, ferries ('traghetti') and fast ferries ('traghetti veloci') to Ischia Porto - the majority of these stop at the island of Procida on the way.

Medmar run ferries to Ischia Porto

SNAV run hydrofoils to Casmicciola, all via Procida

For the most part, hydrofoils are quicker (about 45 minutes) but more expensive (fares depend on season - check the various websites for info). On hydrofoil services you may also have to pay for each piece of luggage. The motion of a hydrofoil is quite different from an ordinary ferry particularly when they turn to get in or out of a port. It's usually much better if you can stand outside, but to be on the safe side I would recommend some sort of travel sickness remedy if you're not used to it. Ferries are slower (and obviously the ones that stop at Procida are the slowest), taking about an hour and a half I think, but cheaper, and you don't pay for luggage. It seems to depend a little bit on the company and the boat, but sometimes on the ferries you can find yourself dragging luggage up narrow stairs, whereas on the hydrofoils there's a luggage area. But it really does depend and usually you find you can cope. The ferries have at least a little bar serving drinks and panini. Not sure about the hydrofoils as you're never on them for long! All the boats have toilets though - be warned it's an interesting experience using the bathroom on a hydrofoil if it's turning or if the sea's rough!

Other ferry services run from Pozzuoli to Ischia Porto (run by Medmar and by Caremar - the latter via Procida) and to Casamicciola (Medmar). Other hydrofoils run from the smaller port of Mergellina to Ischia Porto and Forio (Alilauro).

Timetables etc depend on the day of the week and the season, so check the websites if you need to be there at a certain time. For the return trip, if you have a flight / train to catch, leave yourself enough time to allow for queueing for a taxi or waiting for a bus at the port. Boats are generally on time, as they have a small time slot to get in and out of the port at Ischia. But sometimes the bigger car ferries can be delayed if there are a lot of large vehicles boarding particularly at the Ischia end, where it can be pretty chaotic. To be sure of the timetables for your return journey you can ask at the ticket offices at the port in Ischia. There are usually posted timetables, or just ask at a window.

Once you've arrived in Ischia, it entirely depends where you're going as to your best way of getting there. There are always taxis available at Ischia Porto and, I would imagine, at Forio and Casamicciola. If you're only going a short distance (e.g. to Ischia Ponte from Ischia Porto) there may be a 'microtaxi' - a little three wheeled affair with next to no suspension. Quite funny though! I found taxis reasonably expensive, though, and the bus services are very good. From Ischia Porto, the main bus stand is just back a street or two from the port (hard to explain precisely where it is, as it depends where the boat docks, but ask someone when you're there), and you can get a bus to pretty much any of the biggest towns - list of bus services here (scroll down to 'area di Ischia'): SEPSA website.