Motorships to Marina Grande: from Naples (Molo Beverello) and Sorrento run several times throughout the day, from Amalfi, Positano, Marina del Cantone and Ischia run daily in the summer. Almost all of the services departing from Naples transport cars, although in the summer, only the island residents have permission to drive around.
Hydrofoils to Marina Grande: from Naples and Sorrento run a few times throughout the day, from Salerno, Amalfi and Positano run once a day in the summer.
Those flying to Capodichino can use the spacious comfy shuttle service that will take them from the airport to Piazza Municipio, near Molo Beverello.

When flying to Rome, you can reach Termini station by bus, train or taxi and then board a train for Napoli central station. From Napoli central station, take a bus or taxi to Molo Beverello.
A further option is to get off at the Mergellina train station where one can reach the homonymous peer with a pleasant five minute walk and then board for Capri.