When I was looking through re-upholstery guides before working on my dining chairs, I didn't find many helpful bits on folding corners. When it came time to do them, after stapling the sides of my fabric down, I was at a loss. Luckily, I had two chances to get it right, since I hated my first chosen fabric and stapled a new fabric over it.
A few bits of info before getting started. I used 2-inch foam on my plywood slipseat, with 1-inch dacron batting on top. This made for a pretty thick, cushy seat, and corners that were exceptionally difficult to fold. Here is what I did (the second time around).
1) Staple the side of the fabric down. Start in the center of one side, then staple the opposite center, then the remaining centers, then staple out from those (smoothing and tugging the fabric along the edges as you go). Stop a few inches from each corner.
2) Make a small pleat and fold one corner over so it's parallel to the opposite edge. I made my fold with the pleat facing the side of the seat, not the corner. Staple it down once you have a satisfactory pleat, making sure to tuck excess fabric inside the fold to ensure a smooth edge. This is really difficult to explain, so hopefully the picture will be be helpful:
3) Your next fold will be from the other side of the corner, tucking the fabric in the same way you did the first fold. That is, both folds will go the same direction. The second fold will be stapled perpendicular to the first one. See how in the first picture I'm able to pull the fabric taut from the right side? That's how you get a clean corner and clean, tight edge.
4) Staple like a madwoman (madperson?) to ensure the fabric stays nice and tight and neatly folded away. You can always trim the excess fabric, and no one will ever see the mass of staples. You should end up with something like this:
Not too bad! Not perfect, but considering how much padding I was dealing with, it was the best I could do. Just tuck and pleat until you're happy with the fold, and then staple! Worse comes to worse, you can always pry the staple out and try again. Happy cornering!