Hi Joan,
Quite a few of the tavernas, hotels and rooms offer free wifi which is probably your best bet. I believe Vodafone Greece offer a monthly package of a usb dongle and a months access ut it's quite expensive, about 50 euros I think and you have to buy it from a mobile phone shop in Corfu town. Terry W may have more info which I'm sure he'll post when he reads your post but as I said, wifi is probably your easiest and cheapest bet.