We advise you to book a flight to Athens. From there a domestic flight departs to Skyros several times a week. From Athens also the harbour of Kymi is easily reachable, from there a ferry departs daily for Skyros.
In 2012 the company Sky Express (www.skyexpress.gr) operated a flight from Thessaloniki to Skyros twice a week. At this moment their schedule for 2013 is not yet published.