There are daily flights from Athens to Limnos (ATH to LXS) modern airport facilities with the bigger runaway in Greece.
There are also flight connections with Thessaloniki, Mytilene, Chios, Icaria, Samos and Rhodes four times per week and charter flights connecting various European cities to Limnos.
There is a direct shipping access from: Laurio port of Athens 4 times per week (9 hour journey), Kavala 6-7 times per week (3,5 hour journey), Thessaloniki and Piraeus 1-2 per week.
Limnos has an excellent road network of aprox. 200km connecting Myrina (islands capital) with all the villages, beaches, touristic sights etc.
Buses service the whole island (well most of it), they are cheap, but they aren’t so regular.
Taxis are available all around the island of Limnos. Taxi ranks are found at the central square (KTEL) in Myrina, the airport and the port.
Numerous car and motorbikes rental agencies are scattered in the island. Renting a car is probably the most convenient way to see the island.