Once at the railway station near Piazza Garibaldi, you can reach the Calata Porta di Massa piers for ferry boarding, or Molo Beverello for hydrofoils via the different options:
From the ports of Napoli and Pozzuoli, you can reach the islands of Ischia and Procida by ferries and/or hydrofoils, at the port of Molo Beverello (hydrofoils), Calata Porta di Massa (Ferries), or from Pozzuoli (motor vessels and ferries). Here is the Italian link to access the departure times: https://www.traghetti-ischia.info/tratte/ischia-napoli. There are also connections by sea between Ischia and the other islands in the area (Capri and Procida), as well as between the island and the main localities on the Amalfi coast.
Arriving by plane at the Naples Capodichino Airport, you can reach Molo Beverello (Hydrofoils, Alilauro, Caremar and Snav departures, distance 16 km, time about 20 minutes - via the motorway or by sea - or distance 10 km, time about 27 minutes - via the city centre, using taxis or buses. From Naples Capodichino Airport, to Naples Porta di Massa or Molo Beverello, you can use the ALIBUS service, which is the fast connection between the airport and the city centre.