You may reach Zakynthos by Plane or by Car up to Killini port and then take the Ferry Boat, which departs several times on a daily basis.
During the summer months, there are daily routes also to Pessada in Kefalonia from the port of St. Nikolas in Volimes.

BY PLANE
From Athens from the airport 'Eleftherios Venizelos', with daily 45 minute flights.
Also during the tourist period (April-October), Zakynthos has direct service with many European cities with international chartered flights. The airport in Zakynthos is 4 kilometers from the city, 11 kilometers from Planos - Tsilivi and has an excellent transport network with it.
Learn more here: Olympic Airlines

Below is a list of airlines or tour operating companies which offer charter flights to Zakynthos Zante island, Greece.

Excel Airways: www.xl.com/
Avro Airways: www.avro.co.uk/
Freedom Flights: www.freedomflights.co.uk/
Thomson: www.thomsonfly.com/
First Choice: www.firstchoice.co.uk/
Thomas Cook: www.thomascook.com/
Olympic Holidays: www.olympicholidays.co.uk/
My Travel: www.mytravel.com/
CharterFlights: www.charterflights.co.uk/
CheapFlights: www.cheapflights.com/
HolidayWareHouse: www.holidaywarehouse.co.uk/

BY BOAT
With buses of the KTEL of Zakynthos which have daily service and directly connect Zakynthos with Athens, Patra, Thessalonica and via the strait of Kyllini (across from the coast of the Peloponnese) with Zakynthos.
This sea voyage lasts one hour and is carried out by a ferryboat on approximately an hourly basis during the summer months and five times a day during the rest of the year. Zakynthos is also connected to the surrounding islands of Kefallonia and the Peloponnese (Kyllini).
Learn more here: Zante Ferries & KTEL Buses Zakynthos