Choose treated boards that are the same dimensions as the damaged joist. Hold each of your new boards against the existing board it matches. Mark the new lumber with your pencil so your cuts will be true.
Use your circular saw to cut each of the new boards. Follow your pencil marks to get the appropriate length and angle on every board.
Have an assistant hold the damaged boards in your old joist in their original position. Use a bottle jack to lift any pieces that your assistant can not lift by hand.
Hold each new board beside the board in the old joist that it will be replacing. Use your hammer to drive 16d framing nails through the old board and into the new one to secure the new wood. Drive a nail every 12 inches along the length of each board.
Attach a second piece of new wood on the opposite side of the old joist. Drive a nail through the wood every 16 inches to secure the second part of your new frame and complete the repair.