Remove all the furniture and accessories from the room so you can access the flooring. If you have one heavy piece of furniture that you can't remove, slide it to a corner of the room where it won't be in your path as you work.
Remove the baseboard molding closest to the broken floorboard. Insert a crowbar behind the nail that's holding the molding in place. Pull the nail away from the wall without damaging the drywall behind it. Repeat on all the nails until the baseboard is free. Set it aside.
Pull up the good laminate flooring piece by piece by pulling it up and out to unlock each board. Set each board aside where it won't get damaged.
Remove the damaged piece by unlocking it. Set it aside but don't get it mixed up with the good pieces. Replace the board with either a new or original board. If the broken board is in a central location, use an old board so the wear-and-tear of the board is consistent with the room. If the location if off to the side, replace with a new board.
Lock the flooring back in position by pressing the connecting sides together until they click and setting the board in its original position. Continue until all the flooring is in place.
Attach the baseboard molding to the wall using nails. Use the original nails if they are still in good condition or remove and replace them if they were bent.