From the airport Napoli Capodichino you can arrive at the port of Molo Beverello using a taxi or the public bus. A shuttle bus connects the airport with the port of Molo Beverello , the ticket can be bought on the bus. Taking a taxi you can also reach the port of Mergellina and take a hydrofoil from there to Ischia. Once arrived on the island take a taxi to the hotel or get on the public bus to Ischia Ponte.
The stations of Napoli Centrale or Mergellina are both not far from the ports. The main station Napoli Centrale is about 2 km from the port Molo Beverello can easily be reached by taxi or public bus for which you can buy the ticket inside the train station. The station of Mergellina is about 500 m from the hydrofoil port of Mergellina and can be reached by taxi or you can walk there. Once arrived on the island take a taxi to the hotel or get on the public bus to Ischia Ponte.
Take the highway to Naples: after the toll station follow the highway for about 12 km and take the exit "Tangenziale" in direction Pozzuoli, follow the "Tangenziale" and take the first exit after the toll station "Via Campana", following the indications to the port to embark to Ischia Porto o Casamicciola Terme. Choosing Calata Porta di Massa (the longer crossing), after the toll station follow the indications for "Napoli - zona portuale" and then the indications "Imbarco per le Isole" to embark for Ischia. Once arrived on the island follow the indications to Ischia Ponte.