Dumpster chairs, even. Scott and I were moving out of our apartment and found these wonderful bar chairs just sitting by the dumpster on our way out. There was nothing wrong with them, and they were free. I'll take 'em! That was 7 years ago, and they're still going strong, especially with my latest project.
I started by detaching the seat from the frame and beginning the long task of removing the staples from the fabric.
I tried to work all 4 corners to be as flat as I could manage, and they all had extra stapling. It was more trial and error than anything. I had to take out staples a few times to rewrap. At this point, while you're wrapping, it might also be a good idea to mark the existing screw holes on your fabric so you don't staple them and so you know where they are for reattachment. I didn't mark them, but everything worked out fine.