Steps:1. Check the angles for the replacement piece. For irregular angles that aren't 90-degrees, use a sliding T-bevel to measure the angle. Adjust the bevel to match the angle, then lock it down (figure A). This will be used as a template for cutting the new piece.
2. Measure for the width of the piece, and be sure to take into account how the board will be positioned. If it's mounted at an angle, make sure your measurements are taken from the board's final position.
3. Measure for length. For precise measurements, use a folding rule with sliding extension (figure B).
4. Transfer measurements to the board. Use a combination square to draw a perfectly straight line to mark your width (figure C).
5. Clamp the board onto a scrap piece of lumber and make the cuts using a circular saw (figure D).
6. Drive a few nails through the replacement board into your scrap board to secure it, then remove the clamps. Attach a rip fence to the saw and make the lengthwise rip cut (figure E). Use a hand plane to shave away the top of the board to accommodate odd angles.
7. Back inside, chip away any plaster or drywall mud around the opening that may interfere with a tight fit.
8. Fit the replacement piece into place. It should be a little snug. Tap it into place using the handle of a hammer (figure F).
9. Pre-drill holes for nails using a hand-operated push drill.
10. Attach piece with finishing nails and drive nail heads below the surface with a nail set. Cover nail heads with putty.
11. Run a bead of caulk along the seams (figure G). Prime and paint the piece and you're done.