If you’re flying in to Skiathos, you can take the ferry over to Loutraki. The ferry quay in Skiathos is at the south end of the harbour. It’s only 5 minutes taxi ride from the Airport. Alternatively, your charter company may offer to pick you up by water taxi from Skiathos.
If you’re arriving via the combined bus and ferry service from Athens, the ferries call at Loutraki after Skiathos, so you can book right through.