This is actually a fairly easy process if you have a few simple tools. You can do it yourself if you're so inclined. First, select foam made from compressed polyester fiber. I like Nu-Foam, but there are other varieties out there. This is a better material than the more common polyurethane foam because it is flame-retardant, mildew-resistant, non-allergenic, washable, and it doesn't yellow or disintegrate over time. This means it will last longer and wear better than polyurethane. You can get compressed polyester fiber foam in a variety of precut sizes, and it can always be cut down if it's just a little too big, so it's convenient as well. If you have to cut the foam, use a utility knife or even sharp scissors to get an even cut.
Select a fabric that you enjoy. An upholstery fabric is your best bet, but you can use almost anything. Bear in mind that thinner fabrics aren't as durable and will have to be replaced more often. Thicker fabrics wear better and are more designed for constant use.
Once you have your foam and fabric, turn the chair upside down. Look for the screws holding the seat in place and unscrew them. Remove the seat and place it in front of you so you can see the staples holding the existing fabric in place. Use a heavy-duty staple remover (or a flathead screwdriver) to remove the staples. Do this carefully so you don't damage the seat.
Take the existing foam pad and fabric off the chair. The foam may be disintegrating, so be careful not to make too much of a mess. You can throw out the foam, but keep the fabric for now. You can use it to create a pattern and limit mistakes. Press the fabric with a warm iron so it lies flat. Place it on top of a sheet of butcher's paper (or other large paper) and trace the shape of the fabric. use a thick marker so you can see the line clearly. Then cut out the shape and discard the fabric.
You now have a basic pattern to use with your new fabric. Position the new seat fabric right side up on a flat surface. Put your pattern on top and trace the pattern using a removable fabric marker to avoid staining the new fabric. Cut out the fabric and discard the pattern (unless you're doing more than one chair).
Place the new foam on a flat surface. Put the seat base over the foam to see if you have to trim any edges. You probably do, even with precut pieces. You probably want to round the corners and trim the edges. Use your scissors or a sharp utility knife for this.
Now that everything is trimmed to size, place the fabric right side down on a flat surface. Center the foam over the fabric and place the seat base over the foam. Pull the fabric taunt toward the seat base along each side. Place a staple in the center of the edge closest to you. Pull the fabric taunt again and place a staple in the center of the edge furthest from you. Do the same on the right and left edges, pulling taunt each time. You should have four staples holding the fabric in place.
Now finish stapling the fabric, folding the raw edges and corners under as you go. Start close to one of your staples and move toward the corner, pulling taunt each time to keep the fabric smooth. Make a small pleat at each corner, then staple the pleat in place. Don't cut the fabric or you'll risk a tear in the finished product.
When the fabric is attached and you're satisfied with the results, reattach the seat to the chair frame. Repeat with all your other chairs and you're done.
A word of warning: If the fabric you're using has a pattern where direction matters, make sure you staple the fabric so the pattern goes the same way on all chairs. It will look more professional.
Want to watch a professional do it? Take a look at the video below. Bear in mind that he doesn't remove the foam or existing fabric, but you get the idea.