Let's get rolling, no?
We were lucky enough to find chairs that were in good shape and had good bones- we probably paid a bit more for that, as I'm sure you've seen how cheap destroyed furniture can go for, but I think it's worth it, at least for my first bigger project. The wood was well cared for, and most of the padding was solid (we did need to replace the arm pieces, though). I would gravitate towards foam padding if you can, because fixing springs is a wholeee different ball game. If the padding was in bad shape, like the kitchen chairs I redid a few years ago, it's inexpensive and pretty easy to replace. If you aren't as lucky and your piece needed some help, now would be the time to strip the finish, sand down the wood, re-stain, and then condition or coat with a protective layer. Once that was done, cut your padding to fit (again, much easier if you retain the original) and attach it.
I didn't get a shot of the chair completely stripped, but here she is with the start of the arm upholstery.
For this project, I used a good amount of spray adhesive, which you can get at any hardware store, for fabric and foam. I would use that, plus well-placed staples, to attach your foam. Once the fabric is in place, it will hold things together.
Next Tuesday (my favorite day for original content, clearly) we'll go over the upholstery, then it's attaching trim and the finished project!