Re-covering a scooter seat, even an older one such as a Vespa from the 1980s, is fairly straightforward and only involves a few necessary parts. However, if those parts are missing, it makes the restoration almost impossible given the way Piaggio, the Vespa scooter manufacturer, made the seats.
Unbolt the existing seat from the scooter using a socket wrench and the appropriate socket (either a 13mm or 11mm socket, depending on the scooter model). Place the seat itself on a work bench or table. Turn the seat upside down to expose the underneath cavity.
Remove all the vinyl clips on the underside of the seat and put them in a cup for temporary safekeeping. Pull the seat cover out and apart from the seat foam and frame. Remove it completely once separated and throw the old cover away. Review the seat foam to find any gouges or missing sections.
Take some other foam and glue and appropriate piece cut with scissors to fill any missing spots in the seat foam. Glue the replacement section into the seat foam to fill the missing space properly and keep it attached.
Lay out the new seat cover over the seat foam and frame in the right direction, with the nose piece in the front and flat wide part in the back. Flip the whole seat over so that the new seat cover is on the bottom with the foam and frame on top. Pull the edges of the seat cover up and over the edge of the frame and fold it back inward toward the frame cavity in the centre.
Reinstall the cover clips all around the seat frame so that the new seat cover pulled up stays in place. Pull the cover tight so there is no slack. Readjust the clips if necessary. Turn the seat right side up again to check your work.
Move the now covered seat back to the scooter frame and line up the hinge plate to re-bolt it to the scooter. Install the securing bolts and tighten them with a socket wrench. Lower the seat and secure it on the rear seat hook already installed on the scooter frame.
If you want a custom seat with different materials vs. what you get with an aftermarket stock cover, you can always take the seat frame and foam to a professional upholsterer. Many of the custom seat covers far exceed the quality of stock replacement covers. However, the price of the work can be three times the cost.
Avoid using any kind of heat application such as a blow dryer or glue gun. Replacement seat covers tend to be made of thin layers of vinyl which warp and melt easily.