Empty the contents from the desk. Lay a large blanket on the floor. Tip the desk onto its side or back to access the loose desk leg.
Place the appropriate type of screwdriver into the slot on the screw head and turn the screws to the right to tighten them. If glue holds the desk leg, place a thin wood chisel on the line where the leg meets the underside of the desk. Lightly tap the chisel with a mallet to loosen the glue between the leg and the desk.
Use a scraper to remove old, dry glue from the joint.
Sand the joint and the top of the desk leg with 100-grit sandpaper to expose the bare wood. Wipe the desk leg and the joint with a tack rag to remove the dust.
Spread wood glue over the joint and the top of the desk leg with a paintbrush. Fit the leg back into the joint. Clamp the desk leg in place with a hand screw clamp. Leave the desk on its side or back until the glue sets, which generally takes from six to eight hours.
Empty the contents of the desk. Lay a large blanket on the floor and turn the desk to its side or back to reach the broken leg.
Remove the screws that hold the broken part of the desk leg in place. If glue holds the desk leg to the desk, place a thin wood chisel on the glue line and tap it with a mallet to free the desk leg. Scrape the old glue from the joint with a scraper and sand the surface of the joint with 100-grit sandpaper. Wipe the joint with a tack rag.
Fit a new desk leg that matches the size and height of the remaining desk legs into the joint. Mark the placement of the screws on the leg with a pencil, if a bracket and screws hold the desk leg to the desk. Drill pilot holes into the leg with a drill. Insert new screws through the bracket and tighten the screws with the appropriate screwdriver.
Drill a 1/4-inch hole 1 inch deep into the top of the desk leg, if glue holds the leg to the desk. Drill a 1/4-inch hole 1 inch into the frame of the desk. Cut a 1/4-inch wood dowel into a 2-inch section. Dip half of the wood dowel into wood glue. Insert the wet glue end into the hole on the base of the desk and tap the dowel into the hole with a mallet. Spread wood glue over the joint, protruding the dowel and top of the desk leg. Place the drilled hole on the leg onto the protruding dowel and tap the bottom of the leg with a mallet to fit the desk leg tightly into place. Clamp the desk leg into place with a hand screw clamp. Let the wood glue dry for six to eight hours.