Are you talking about a coaster? Or is there a special type of design you are looking at?
With a fabric coaster, you start out with a piece of stabilizer in your hoop. You stitch out the placement lines, and then put down your fabric. I use a dot of glue stick to keep it from shifting, as the spray adhesive is out of my price range. You may want to add a bit of batting underneath to give it some absorbency (cotton batting or a piece of flannel works great here). After you stitch that out, remove the hoop from the machine (do not unhoop your stabilizer) and clip closely to the edges. Put the hoop back in and stitch your designs. When you are finished with the top decorations, remove your hoop again, place a piece of fabric on the bottom of the hoop (again with a dot of glue to hold in place) and then stitch around again. Remove the hoop and trim. Then place the hoop back in the machine for the final satin stitching around the edges.
I hope this helps.