As with most floors, you should regularly sweep and vacuum parquet and occasionally go over them with a damp mop. Since it is wood, the mop should be lightly moist. Cover the floor with rugs to help protect it, especially in heavily trafficked areas near the entrance door and perhaps in the kitchen. Wipe up spills with a cloth. You can remove scuff marks using a a fine steel wool pad and a floor cleaner. To touch up small areas, use one of the specially made wax sticks in the same color as your floor. Color the area with the stick, scrape off any excess and buff the area with a soft cloth. Avoid wearing high-heeled shoes on the floor, as they can dent or scratch the floor. Do not drag furniture across a wood floor. Lift the furniture, and if possible put wood protector covers underneath the legs of your furniture.
Parquet floors often fade in spots, usually due to wear and tear of the varnish or polyurethane finish. You can refinish these floors, by sanding and then applying a new coat or two of polyurethane sealer. Sometimes there is water damage or discoloration to a small area. In this case, you can repair just that area. Put some masking tape around the damaged area, and then sand, stain and put on a new finish.
If you have missing pieces in your parquet floor, take a piece to the home improvement store and find the best match in color and grain to use in the repair. Have the new piece cut to the right size and shape, and use a polyvinyl glue to hold it into place. Sand and refinish that section of the floor, and it should look like new.
You can also refinish the entire parquet floor by sanding and then finishing with several coats of polyurethane. With a large area of flooring you should have a professional refinishing company look at it and give you an estimate. Depending on the state of the floor and your budget, you may prefer to have the refinishing done professionally.