Finally something I can give some advice on! Sewing on a patch is simple, since it doesn't involve a lot of heavy stitching, but most of the time they come with an iron-on backing and if it doesn't Wal-Mart or Jo-Ann's/Hobby Lobby/Micheals ect will sell something you can iron on the back of the patch, peel off one side, and iron the patch on. That is not a permanent solution, though! Here's how I would do it:
1) Iron the patch on.
2) Find a thread that is similar to the thread used to stitch the edge of the patch.
3) Place some stitches around the edge, going in the same direction of the patch stitching.
It's really easier to do that to explain. If you lived in my area I'd do it for you.