By Air: Normally in the Spring and Summer Sky Express operates two flights a week between Athens and Skyros, and two between Thessalonika and Skyros. The flight time is approximately 35 minutes and the return cost is around €100 - €150. Whether you can book a flight to Skyros depends on the availability of flight schedules. At some times of year, particularly during winter months, no flight schedules are available.
By Land and Sea: Land and sea travellers should take a bus from Athens to Kymi, and the ferry from Kymi to Linaria on Skyros. The bus journey is long but very restful, going overland via the north of Evia. There are two ferry sailings a day from Kymi to Linaria - you should check with a travel agent or locally in Athens before sailing.
Skyros (+44-1983-865566) organises holidays for mind, body and spirit in Skyros town and more laid-back packages in Atsitsa on the west coast of the island. Their recommended transfer is organised by Hellenic Travel and costs approximately 40 Pounds each way. This includes coach from Athens to the coast, ferry to Evia, coach across Evia to Kymi, and ferry from Kymi to Linaria on Skyros. It takes approximately five hours.
More details about travel and accommodation can be found in the Lonely Planet Guide to Greece (pages 654-659 of the 2006 Edition).