Laminated flooring clicks together and floats over the subfloor, which can be any flat, dry surface. When the subfloor is plywood or concrete, you often have to level out imperfections and lay a moisture barrier before laying the laminate floor. Neither procedure may be necessary when you lay the floor over an existing parquet floor. Unless some of the tiles are bulging, the surface is already flat and in all likelihood has an adequate moisture barrier underneath it. A significant number of loose or missing tiles, though, may indicate the need for a new moisture barrier.
Sand down any bulging tiles with a belt sander and a 100-grit sanding belt. If any tiles are loose, glue them back in place with construction adhesive. If a significant number of tiles are loose or bulging, it may be a sign that there isn't enough moisture protection, especially if there is a concrete subfloor under the parquet. If so, protect your new floor by laying a plastic or vinyl moisture barrier on top of the parquet and stapling it down with a staple gun.
Start laying the flooring along the most prominent wall running in the same direction you want to run the flooring. Click the boards in the first row together end-to-end, leaving an expansion gap of 1/4 inch between the flooring and the wall.
Assemble boards by lifting the end or edge of one and pushing it against a board on the floor. Lower the board when the tongue interlocks with the groove on the other board and they will snap together.
Measure the gap for the last board with a tape measure, measure and draw a line on the back of a board and cut it from the back with a circular saw to avoid chipping the surface. Drop the last board in the gap between the floor and the wall and pull it in place with a laminate pull bar, which is a special type of pry bar made for installing laminate floors.
Cut off the bottoms of door jambs so you can slide the laminate flooring underneath them. Place a piece of laminate flooring on the parquet subfloor, push it against a jamb and draw a line on the bottom of the jamb. Cut through the line with a hand saw.
Assemble boards until you reach the wall opposite the one from which you started and a gap less than the width of a board remains between the flooring and the wall. Measure the gap and cut boards to that width on a table saw, allowing for a 1/4-inch expansion gap. Place each board in the gap and pull it into the floor with a pull bar.
Install baseboard around the perimeter of the floor when you are finished installing the flooring. Nail the baseboard to the studs or bottom plate of the wall, not to the floor, with 8d finish nails. The baseboard will hide the gap around the edge of the floor and also hold the floor down.
Cut notches to fit the flooring around door jambs and other obstacles with a jigsaw fitted with a metal-cutting blade. The fine tooth blade isn't as likely to chip the surface as a woodcutting blade. If you have a hard time assembling boards, tap them together with a mallet. Laminate flooring dealers have plastic tapping blocks to place on the edge of a board you are tapping so you don't damage it.
Wear safety glasses when cutting laminate flooring with a power saw. It is usually made of a combination of wood chips and plastic, both of which produce shards that can damage your eyes.