There are flights from various European towns of Italy, Germany, Austria and UK to Nea Anchialos, a small airport close to Volos, with Ryanair or AirBerlin. Upon your arrival at the airport of Nea Anchialos, public bus service connects to the port of Volos and take a ferry or Flying Dolphin from there.
From Athens you can buy a combined bus/ferry ticket which will take you overland to the port of Agios Constantinos, where you can transfer to a boat to all three Sporades islands. Olympic Airways during the Winter (November to April) operates 2 Schedule flights a week (on Sunday and on Thursday) from Athens to Skiathos. In summer (May to October) flights from Athens to Skiathos are made daily.
If you have your own car, you can drive to Volos, Agios Constantinos or Kimi on the island of Evvia and take a car ferry from there, but bear in mind that not all scheduled boats carry cars, so you'll need to verify in advance which ones do.
Only Skiathos has a commercial airport, but once you get there you'll find frequent boats to the other Sporades. From May to October there are charter flights to Skiathos from most regional airports in the UK, Scandinavia and Italy.
Hellenic Seaways - Itineraries 2013