Pull the old vinyl off the seat by removing any staples or nail holding the vinyl on the bottom side. Lay the vinyl on a large piece of newspaper and trace around the outside edge to make a pattern.
Lay the pattern on a new piece of vinyl and cut it out. Place the vinyl with the top side facing down on a sturdy table. Check the padding on the seat to verify it's usable. Cut a new piece of 1-inch-thick foam to the size of the seat if you need to replace the padding.
Set the foam and the chair seat on top of the vinyl so the bottom of the seat is facing upward. Grab one edge of the vinyl and pull it to the bottom of the seat. Place one staple in the center of the edge to secure. Repeat this process with each edge of the seat.
Secure the remaining vinyl along each edge of the seat with staples up to 1 inch from each corner.
Secure each corner by folding over one side to the bottom of the seat. Staple two or three staples into the vinyl to hold it in place. Fold the other side of the corner to the bottom side of the seat and staple it in place. Repeat this process with each corner.
Secure the seat back on the frame if you were able to remove it for recovering it with vinyl.