Complex parquet floor patterns can best be appreciated when the finish is shiny and defect-free. You can maintain this finish with wax, but over time wax will collect dust and turn yellow, so you periodically have to remove it if you want the floor to return to its natural colour. To get the best sheen without wax, knock down the surface of the floor with a floor buffer fitted with a sanding screen, then spread a light coat of new finish and buff it up with polishing compound and a lamb's-wool buffer.
Clean the floor with a hardwood floor cleaner and a mop. Mix the cleaner with hot water according the specifications on the container and mop the floor liberally to remove old wax and dirt. Let the floor dry completely.
Fit a floor buffer with a 150-grit sanding screen. Set the buffer flat and remove the nut in the centre of the pad with a wrench. Place the screen on the pad and tighten the nut, then stand the machine up and plug it. Hold it steady when you turn it on and let it glide over the surface of the floor. You can steer it with gentle pressure on the handles.
Screen the entire floor, then vacuum the dust away and clean the floor with a moist tackcloth.
Test the existing finish so you can tell what type of finish to use to touch it up. Pour a little acetone on a cotton swab, moisten a small, inconspicuous area on the floor with it, then look at the swab. If it is sticky, the floor finish is varnish. If it isn't sticky, the finish is polyurethane.
Thin the appropriate finish with about 20 per cent acetone and spread it on the floor with a floor finish applicator. Let it dry for the time recommended on the container.
Remove the sanding screen from the buffer and attach a lamb's-wool buffing pad. Spread polishing compound on the floor and buff it to a sheen with the floor buffer.
If your old floor finish is polyurethane, touch it up with water or oil-based polyurethane. If it is varnish, use varnish.
The flooring buffer can give you a wild ride until you are used to it. Stay in the middle of the floor until you master it and don't let it slam against the walls, or it will make marks.