Dassia is around 13/14km from Corfu Town, and a similar distance from the airport.
There are taxis across the road when you come out of the arrivals terminal. get a price (including the luggage), think this should be around 25 Euros.

A little info re airport to Dassia
http://www.dassia-corfu.net/

If you fancy the bus from Corfu town to Dassia, here's the blue bus timetable (no 7) from San Rocco Square in the Town
http://www.allcorfu.com/ou-buses.html

Have you checked with your Dassia accommodation if they do a transfer service?

Thanks Phoebe, thats really helpful. I will enquire if hotel do transfers also, although we weren't offered one when we booked.