Center the vinyl on the seat of the chair and flip the seat upside down on a hard surface. Secure the vinyl to the seat by pulling the it tight and placing one staple on either side in the center of the seat. The vinyl should be at least one and a half inches wider than the seat of the chair on all four sides.
Continue to secure the vinyl by pulling it and alternating staples on all four sides of the seat. By alternating staples, you can assure there will be no bulges when you are done. Periodically flip the seat over to be sure the vinyl is tightly fitted.
Place your four fingers at the corner of the seat and gently fold the vinyl over the edge. Curve your fingers around the corner, pulling the vinyl tight and using your thumb to hold it in place. Be sure not to stretch the vinyl so much that it begins to discolor or loses its elasticity.
Continue smoothing the corner a few more times with your fingers. Once you have the corner smooth, staple the edge of the vinyl to the seat with two staples on either side of the corner and one in the center close to the tip of the corner. Repeat the process for each corner of the seat.