Mark a line down the middle of the bad floor board with a pencil and a straightedge.
Drill several holes along the line using a 7/8-inch spade bit.
Insert a chisel near the holes in the board and split the board using a hammer and the chisel. Pry up the old bits of board.
Measure the depth of the hole, width and length. Bring the old piece of wood to the lumberyard to have the wood material matched and a new board ripped to size.
Remove any nails from the floor in the entryway using a pair of pliers.
Insert the new board into the hole and drive a nail every 11 inches along the board about 1/2 inch from the edge of the board. Drill pilot holes for each nail to prevent splits in the board.
Paint or stain the replacement board the same color as the rest of the floor.