Take off the floor trim around the perimeter of the room, using a hammer and pry bar. Keep the trim intact as you remove it. There should be a 1/2-inch space between the edges of the flooring and the wall that is revealed after the trim is removed.
Wiggle the boards that are next to the wall nearest the damaged area, using your hands to move them until they come apart from the boards next to them. Let the the loosened boards sit in the space along the wall in the same order they were in while they were connected. Loosen the entire course along the wall.
Repeat the process of loosening the boards on the next course, and the next, leaving all the boards in the same order they were in while they were connected. Work your way out across the floor until you get to the damaged area.
Take out the damaged boards. Snap the replacement boards in place where the damaged boards were installed, locking them to the adjacent boards by the fittings on their sides.
Put the floor back together in the reverse order of how it came apart, snapping the floorboards to one another course by course, working your way back to the wall where you started.
Reinstall the floor trim, using a trim nailer. The trim will hide the spaces along the edges of the floor.