Have a new seat cover to install yourself? You can 'tune-up' that old base if it's not too far gone. The wood on the bottom of this seat wasn't rotten, just cracked in a couple spots where the seat brackets attached to the frame. Brass braces reinforced these two spots. Also, never hurts to carpenter wood glue this and any support pieces that attach to the plywood base. Add screws to strengthen where needed.
Seat foam can crush down and split over the years. I used a man-made (not synthetic) thin carpet pad to build the seat top back up and cover foam defects. Use 3-M 777 adhesive to adhere the pad pieces so it won't shift out of place when installing the cover.
Work slowly from one end of seat to the other when stapling cover edges to the bottom, a little at a time to keep things taut and square. An electric stapler should work just fine, unless you have access to an air model. Be patient, and have a tack hammmer handy to drive any errant staples flush. Rivet and/or glue the vinyl to metal covers.
Cover before: Galvanized mount brackets after; before using a wire wheel:
Covers after; backrest cover not installed by me, all else was:
A couple of other tips added just before this post are on the bottom of page 3.