Turn the chair upside down and unscrew the seat from the chair. Once you have all screws loosened the seat will come free from the chair. Set the chair frame aside until it is needed later.
Turn the cushion upside down after placing on a hard surface, and use the flat-headed screwdriver to pry loose all of the staples holding the fabric to the seat. Use the needle nose pliers to pull all staples free of the seat, if needed.
Using the old fabric as a template, cut the desired shape out of the new fabric that you will use to cover the seat of the chair. Do this for each of the seats that you are re-covering.
Lay your fabric pattern-side down and place the seat of the chair onto the fabric. Starting with the middle of one of the sections, pull the fabric taut and staple it to the underside of the seat. From that staple every 3 inches pulling the fabric taut and securing it to the seat.
When you get to the corner of the seat, fold the two sides of the corner over like you were wrapping a gift, and secure them to the seat with a staple on each side.
Once all of the chairs have been re-covered in the new fabric, retrieve your chair frame and place the newly recovered seat onto the chair base. Secure it using the screwdriver, with the screws you took out at the beginning.