Just take the catamaran/hydrofoil from Skiathos to Ag. Konstantinos (1.5 hr) on the mainland and then a KTEL bus to Athens (2 hrs). Approx 1-2 per day. There is, I think, also a through ticket with a company that does the same thing but uses their coaches to Athens, at slightly greater cost.
Just ask in the travel agents on Skiathos harbour.
You can also fly with Olympic Airlines.

See this post on the Skiathos Bulletin Board

Ouzo, Naughty, thats great, thank you for yer help.