This week's project is easy, but time consuming. The over-all time isn't a huge commitment, but there are periods of letting things dry before moving on to the next step. It's a pretty project, but not great for last minute.
The things you'll need are some cork backs, broken pieces of tile, pottery, dishes, whatever, tile adhesive, tile grout, and mosaic tile sealant (if you want these to be more resistant to water and other moisture that is sure to affect coasters.)
Once, the adhesive is dry, take an old butter knife or something similar and fill the cracks and edges with the grout. Don't worry if it's a little messy.