Blanket edging

Hi all. My dog, Brody, likes to be on the couch with me in the evenings but my couch is light colored and, even though he gets regular baths, I know he is a little dirty from being outside. So, I bought a piece of nice fleece to make a blanket for on the couch. I'm wondering how I should finish the edges? I don't have a serger, just a regular sewing machine. How would you ladies finish it if it were yours?
Roxanne