I began by hand-sanding the chairs.
Being that these chairs are fairly old, and not wanting to compromise the integrity of their construction, I opted not to use the typical method of deconstructing them and using the old fabric as a template. Instead, I enlisted the help of my eager six year old! I had her sit atop the foam while I traced it from beneath. I then used the first cushion cutout as the template.
I used bronze upholstery tacks. You can find them at most fabric stores.
After approximately three to four coats of quick-drying stain, I nailed down the fabric. Here are the chairs upon completion.