This is an old jacket that my mom had stored away for ages and was about to throw out! With a few couple steps, I turned it into a new Jean Vest for myself. First I started up using a seam ripper and taking off the sleeves.
Hem the arms if you want a cleaner edge.
Take your fabric and cut out an outline of the area you want to cover. Make sure you leave about half an inch more on all edges allowing you to fold over the edges for a clean finish. Pin and sew.
Repeat on other side. I also did the top back of the jacket.