There are several ways of reaching Kefalonia, the easiest being to fly direct to Kefalonia airport. There are other ways if you have more time, less money or just want a more interesting route. First get a flight to Athens- then get a domestic flight to Kefalonia or neighbouring island. Lots of ferries travel between the local islands. You may prefer the more scenic route- and slightly cheaper way to finish the journey - travel by train or bus from Athens.
Ferryboats connect the island with Kyllini (1 hr 30 min) and with Patra (3 hrs 30 min).
These connections link also Kefalonia to several other islands, of which Zakinthos, Ithaki and Lefkada are the closest.
From the Airport of Kefalonia there are flights to and from Athens (45 min) several days a week and to and from the nearby island of Zakinthos (20 min).
Port Authority: +30 (26710) 22.224
Timetables do change - so it's well worth checking on availability.
Olympic Airways: +30 (26710) 28.808, +30 (26710) 28.881