Start by removing the broken floorboard using a bolster chisel. Place the chisel in the slot at the end of the board and prise the boards up forcing the nails out of the joist. Repeat this process moving along the side of the board. Place an upturned claw hammer under the end of the board to help keep the gap open. Be carful not to damage ajoining boards.
Caution: once the floorboard has been removed bang the protruding nails out with a hammer to prevent accidents.
Cut the new floorboard to the correct length and place in the gap to test the fit.
Now that the board is cut remove from the gap and check the joists for pipes and electrics. Mark on the floorboard that runs parallel where you are ok to fix new board. Once you are happy place new board in the gap and screw down with 2 x 65mm screws at each end and in each alternate joist if possible.
Note: if the new floorboard is slightly raised above the old boards you can sand it down to the correct height.