Luckily for me, patched elbows are all the rage right now. So I drew inspiration from images like this one:
Found the perfect fabric in my stash and created an oval pattern.
Pellon 805 Wonder-Under transfer web (you can buy this stuff by the yard at most fabric stores. I love it and use it for a ton of projects.)
Follow the directions that come with the pellon: iron on adhesive to fabric.
Peel the back off carefully.
Then I put a piece of fabric behind the hole in my cardigan so the patch could have something to adhear to besides the other side of the arm.
Voila! A patched elbow for my favorite cardigan.