Lay a piece of muslin cloth over the piece of furniture you want to upholster. Trace out the shape of the area so you can use the muslin like a pattern. Fold your fabric in half, and check to make sure your pattern is symmetrical.
Pin your muslin cloth to the underside of your piece of vinyl with straight pins so it lays flat. Add two to three inches around the shape of your pattern so you have excess material to staple to the underside of your furniture. Cut out your shape in the vinyl.
Position the vinyl material over your desired piece of furniture and center it. Flip your furniture upside down if possible. Pull the vinyl taut over the underside of the furniture, and use a staple gun to hold in place.
Repeat around the sides of your furniture, pulling the vinyl taut as you go. If you don't have an electric staple gun, a manual one will suffice. But you might need help pulling the vinyl taut as you use both hands to apply enough pressure to pierce both the fabric and the furniture.
Pull the fabric to attach the corners and curved sides just as you would the straight sides of your furniture. If the fabric begins to pucker, try using a hairdryer at a low setting to lightly heat the vinyl. The heat should help the fabric give so that it can be properly pulled into place.