Stuff you need:
Ceramic tile squares (I found mine in the basement)
Fabric cut the same size as your tiles
Felt cut the same size as your tiles
Glue (I used 3M spray adhesive)
Clear acrylic sealer
Brush a coat of Mod Podge onto your tiles. Place the fabric onto the tiles and smooth out wrinkles. Let dry. Once they are dry, brush a couple more coats of Mod Podge over the fabric, letting them dry between coats. After the last coat is dry, spray with acrylic sealer. I did 2-3 coats letting them dry between each one. Then I turned them over and sprayed 3M glue on the backs of the tiles and attached the felt pieces.
(This photo is from my phone- pardon the icky quality.)
There you have it- easy-peasy homemade coasters. A cheap, cute gift idea, too! You could use scrapbook paper or even photos in addition to fabric.