I made a quickie coaster out of scraps that would certainly look better in some kind of coordinating cotten weave. So lets get to it.
1. Determine how big you want your finished size coaster. I chose 4.5 inches. I cut my fabric in 5 inch squares.
You want to weave them together, keeping the center of them tight.
Then pin if you need to. I chose the time saving method of winging it, and sew around the edge with 1/4 seam allowance. Trim the corners.
Then turn rightside out by pulling the base square through the little hole in the center I told you to keep tight. Use a corner tool or knitting needle to make the corner points sharp. As you can see, i didn't spend too much time on these corners.
Any there you go - a handy coaster. Now go make a set to give away to a friend!