Measure the perimeter of the bottom of your mattress using a measuring tape. Add an inch to each side to allow extra room for seams and snaps.
Cut the cover fabric of your choice with a pair of scissors to match the measurements. Fold all the edges in a half inch and secure with sewing pins every 4 inches or so, all the way around.
Stitch the folded edge all the way around the cover to hem, using a threaded needle or loaded sewing machine. Knot the thread and cut it away with a pair of scissors before removing the sewing pins.
Attach the back ends of plastic or metal snaps, available in craft stores or online, using the directions indicated on the specific snap kit. There should be one snap backing on each corner of the bottom edge of the mattress, and more snap backings every 3 to 4 inches in between each corner.
Attach the front ends of the snaps on the bottom edge of the homemade cover. Again, attach one end to each corner of the cover and every 3 to 4 inches in between. Use the same measurements you used to secure the back ends to the mattress.
Drape the cover over the bed and secure the corner snaps to the mattress first before making your way around the rest of the cover.