Turn the chair over and unscrew the seat cover from the chair. Sometimes the screws are inset into a piece of wood, so you may need a long screwdriver. Reserve the screws to avoid having to buy new ones.
Take the old material off of the cover. The material wrapped around to the backside of the chair cover is often attached by staples. You can use a needle nose pliers to remove these. There may be a piece of thin board attached to the bottom side of the chair cushion--if it is in good condition, reserve it to reuse it.
Lay the seat cover on the fabric you have chosen. Use a durable, stain-resistant fabric in a color that matches the rest of your dining room.
Trace the outline of the seat cover onto the wrong side of the fabric. Cut the shape of the outline, leaving a border large enough so that there is room to wrap the fabric around the edges of the seat cover and secure it to the back.
Fold the fabric over the edges of the seat cover and staple it to the bottom, with the right side of the top of the seat cover touching the wrong side of the fabric. Place the staples at least 1.5 inches inside the edge. Leave all corners of the edges to staple last. When gathering the fabric around the edges, create even pleats as you staple.
Cut away the excess fabric. This will make screwing the chair covers back onto the dining room chairs a lot easier.
Staple the board back onto the bottom side of the chair to cover the raw edges of the fabric.
Screw the new seat covers back onto the frame using the old screws.