These are classic chairs, characterized by their cool perforated vinyl seats. Unfortunately, you've gotta know where to look to find new upholstery and old stiff foam is tough to remove. I'll show you how.

Step 1: Set Up

You'll need:
Scissors, a sharpie, a screwdriver, pliers, a wrench, a bunch of rubber tipped clamps, a metal spackling tool, weights (dressmaker's will work),
a 2-3" paint brush, rags, some newspaper or a drop cloth (this gets messy), Barge cement, and Barge thinner and a ventilator is always a good idea when working with strong adhesives.
Purchase 24" x 24" x 1" Foam and head to your local Auto Upholstery supplier for a yard of perforated vinyl (headliner material).

Step 2: Remove the Seat

Turn the chair upsidedown and look for (4) metal clips bolting the chair frame to the seat. Sometimes these can be obscured by the upholstery, but a generally located in the corners. Loosen the bolts to release the clips. Remove any under dressing, sometimes this panel has labels which you may want to preserve, but usually this fabric is trashed. Carefully lift the screws from the seat and save all this hardware!
With your flat head screwdriver, pry up the small metal tabs around the perimeter of the metal chair pan, releasing the old upholstery.

Step 3: Remove the Old Upholstery Fabric

This is the tough part. I recommend softening the glue with the Barge thinner. Use a pair of pliers to pull the fabric away from the metal. Try not to destroy the original fabric too much, as you'll want to use this as a pattern to cut the new fabric.

Step 4: Remove the Foam

Take the metal pan and it's crumbly foam over to your newspaper or drop cloth.
Put on your respirator because it is time to get agressive with the metal spackling tool. Saturate the foam with Barge Thinner and vigorously scrape as you go. Most of the foam will come off in bug chunks. Then dampen a rag with more thinner and rub the remaining foam and adhesive away.

Step 5: Cut Your New Foam

Lay the foam on a flat surface with the metal pan on top. Trace 1/4" outside the perimeter of the pan with a sharpie on the foam. Cut out Foam.

Step 6: Cut Your New Upholstery

Lay the perforated fabric face down on a flat surface. Using weights, flatten out the original cover as best you can. Try to copy the shape with the sharpie as closely as you can, because those weird tabs end up underneath the metal tabs we pulled up earlier.

Step 7: Barge It Together

Take the pan outside again and don your ventilator. Paint the top seat surface with a generous coat of barge and press the foam to it. Next, brush the edge of the upholstery with Barge about 3/4" deep around the edge. Lay the seat pan and foam face down on the upholstery pattern, making sure the front to back alignment is correct. Working from the centers out, use clamps to pull the fabric around the foam. Work your way around, adjusting as you go. When all of the fabric is pulled suffuciently, resolving wrinkles, you can force the fabric under the metal tabs and bend down to secure. I like to leave the clamps on and let the whole thing cure overnight.

Step 8: Re-Assemble the Chair

Remove your clamps and check to see the fabric is secure all the way around. Bring the Aluminum frame over to your table top and line up the seat with the frame. Locate your original hardware and place the screws in the corner keyholes. If you want to ramp it up here, cut a piece of dark twill to line the bottom of the seat. You'll need four holes punched in it for the screws. Fold the edges underneath the frame, checking to ensure they don't peek out the sides. Attached the clips and tighted the bolts to the screws. Take a rag damp with a bit of thinnner and wipe down the entire frame, removing old marks and scrapes and check your vinyl for any stray adhesive. That's it - you are done!