I bought a chair at a thrift store about 10 years ago. It's a very basic chrome kitchen chair, but I loved it. It was gross and dirty and had nasty orange plaid vinyl on it. I recovered it with red vinyl and used it in my kitchen for a few years, then recovered it again with a purple cabana striped canvas and used it in my office.
The sun and my daughters have since destroyed the stripes and so I spent about an hour recovering it. My husband thought I was crazy, as always, but I came away with a pretty cute little chair and when I get sick of looking at it like this, I'll change it again later.
Notice the lovely artwork from my youngest daughter
Step 1: Remove the seats and back from the frame.
Step 2: Remove old fabric. This is a step process since my chair has the back tacked on, I had to take those off first.
With a flathead screwdriver and needle nose pliers, remove staples.
Pay attention to how the fabric is pleated, so you can put the new fabric on in a similar way.
Step 3: Using old cover as a pattern, cut roughly the same dimensions and shape for the new fabric.
I'm sure the chair had been this dirty for a LONG time, but I refused to notice it until the marker showed up.
Step 4: Pull fabric around the seat (and back) evenly and tack in place with an electric staple gun (or a manual one will work if you're strong enough...which I am not). Tack one side, then the opposite, then the adjacent sides. Pull fabric around each corner to make small pleats (as in the "before" picture above), and tack in place. Make sure the top is smoothly covered and taut. Repeat with remaining seat back pieces.
You should consider me armed and dangerous with a staple gun.
Step 5: Replace the back with upholstery tacks and reattach the seat and back to the frame.