Remember Day 3 and the No Fuss Fleece? Maybe you want just a little tiny bit of fuss after all. One of the most basic stitches that every knitter, crocheter, crafter, but NON-sewist needs to know is the blanket stitch. It's a terrific stitch for finishing edges that don't need a finish for the purposes of stability.
Cut your fleece to the size and shape that you want it. You'll need a sharp needle. Avoid using any yarn that is thicker than fingering. The fleece is often too tightly knit for a worsted weight yarn and you'll find this to be more of a chore than you were expecting. You should also avoid using a piece of yarn that is too long. It's better to have more ends to weave in than to have a ragged looking yarn that has been pulled through too many times or a wicked tangle.
There are lots of decent tutorials on youtube since my wordy description would probably be useless for this.