A refund will depend on the type of ticket you bought. Low price tickets tend to be "no cancellation, no change". Slightly higher price are "no change on outward leg, $xx to change return". I've also come across "change to any time in next six months" and an open ticket which is totally refundable even if you do a no show. Typically, you'll have been told the conditions as you booked and they're likely to be printed on your ticket / eticket / confirmation but it's usually the last thing you think of at the time
Look at the ticket .... call the airline.
If you have travel insurance and the cancellation is due to a reason covered, then you should be able to get your money back (possibly minus an excess) through that route.
Tickets are NOT transferrable - so if you find someone else to take your place, they would get turned back at checkin.
What happened? Wonna talk? Do post or follow up here, to Rhia66 (see her post on this thread) or me or elsewhere on the board. You're not the only one to have had a last minute change in plans so we might have some quite sympathetic ears.
P.S. Lisa and I have wanted to try the Iceland Air thing, stopping off a few days in Rekjavik on the way. They go from Glasgow and London to Rekjavik, the on to BWI (Baltimore) and MSP (Minneapolis St Pauls). Anyone else tried it? Experiences??