1) Procure batting. I got low loft polyester quilt batting that was 81x96 inches. Lay batting over the chair (mine is folded in half once) and use a Sharpie to trace the rough shape you'll want the cushion to be. Make sure batting is flush against the back of the chair so the cushion won't be too small.
2) Cut batting out. Lay the remainder over what you cut out and cut again if there's enough for another layer.
3) See if your batting is thick and comfy enough to be the chair cushion. Mine wasn't, so I also used an old nylon blanket folded over twice.
4) Find an old sheet or other fabric for the outside of the cushion. Spread it in two layers and lay batting over it. Trace with tailor's chalk a couple inches from the batting to leave ease for the seams. Cut sheet out. Mine was borderline on width, so I left the fold in on one side.
5) Sew the two sides of the cover together for about 3/4 of the perimeter of the cover. The open part is for stuffing.
6) The hard part: Stuff the batting and blanket in and try to get fairly flat. I didn't do a great job at this. For one, the batting and blanket both have textures that like to stick to other things, so it was hard to get them to move against each other without folding. In the end, I decided I had gotten it as good as I was going to and moved on. I think sewing the padding to one of the layers of cover would be good, but it was so thick that I don't think my machine could handle it.
7) Sew up the hole. I did it on the machine, but a more patient person could get it to look better by doing it by hand.
It's not beautiful, and since I like beautiful things, I might try to make it more beautiful in the future. For the time being, however, the addition of the cushion has made the chair usable for something other than a coat rack, so I'm happy about that.