Meganisi is connected by ferry (the "Meganisi") to Nidri on the island of Lefkada (40 minutes), with stops at the ports of Vathy and Spilia (Spartochori). In summer, connections also operate from Kefalonia and Zakynthos. Tickets are not required to be booked in advance.
To reach Meganisi, first get to Lefkada, which is connected to the Greek mainland by a bridge. The closest airport is Aktion/Preveza, with seasonal European connections and domestic flights from Athens.
Connections are more frequent during the summer season; always check availability if travelling in other periods.