Things You'll Need
Drill with pilot bit
2-inch spiral finishing nails
Hand-held electric nailer
Hardwood flooring is usually installed by three methods of nailing: hand-nailing the first and last courses, because they're too close to the walls to use power tools; power-nailing the courses alongside the first and last ones, because they're still somewhat close; and installing the whole center of the room with a full-sized pneumatic floor stapler, which can't be used within 3 or 4 feet of a wall but makes the job go very fast once you bring it in. The process is the same for a small closet--except you can't use the floor stapler at all.
Use your hammer and prybar to remove the floor trim from the closet floor. Don't break it, so you can re-use it at the end. Spread your flooring felt over the floor, cutting it to size with your razor knife. Staple it down with your staple gun.
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Lay your level next to the longest wall in the closet and mark a pencil line along it, 1/4 inch from the wall. This will provide a gap between the floor and wall, which you have to maintain all around the closet to allow the floor to expand.
Lay your first piece of flooring on your marked line, with the grooved side facing the wall. Drill pairs of side-by-side pilot holes every foot or so along the board's surface. Hammer 2-inch spiral finish nails into each of the pilot holes. Set them below the surface with your nailset. Cut a second floorboard to size on your miter saw to put at the end of the first one, leaving a 1/4 inch gap at the end, and install it the same way.
Lay your next courses of floorboards by tapping the tongue-and-groove sides of the boards together, holding them tightly in place with your prybar, and using your hand-held electric nailer to sink nails into the sides of the boards at a downward angle. Put a nail about every foot. Cut the end pieces as needed, leaving your 1/4 inch gap at the walls.
Lay all the flooring across the closet floor with your hand-held nail gun, until you get to the final course. Top-nail that course, as you did the first one. Re-install the floor trim to cover the expansion gaps at the walls.
Wear goggles when using a nailer.