Examine the damaged area on the door jamb and measure the width and the height of the area that needs to be replaced.
Lay a 1-by-4 inch board on a work surface and mark the width of the damaged area on the board with a pencil. Repeat the process further down to mark another section for the width of the damaged area. Measure another section further down that is the length of the damaged area. Cut each of the three sections out of the board with a power saw.
Place one of the short boards above the damaged area of the jamb and secure it with finishing nails at 2- to 3-inch intervals. Install the other short board at the bottom of the area and the longer board along the side of the damaged area. These boards will create a frame for the router to move along.
Install a straight cutting bit into a router. Measure the depth from the frame board to the damaged portion of the jamb then add the depth of the 1-by-6 inch replacement board to it. Set the router to this depth.
Plug in the router and put on safety glasses. Insert the bit into the frame boards then turn the router on. Move the router around the entire damaged area to drill it out.
Remove the guide boards by prying out the nails with a pry bar. Cut a piece of replacement wood to the same width and length as the repair site with the power saw.
Apply wood glue to the back of the replacement board in a 1/4-inch layer. Press the board against the jamb and insert a 1-inch finishing nail at the top and bottom to hold it in place.
Add a coat of primer to the repair site with a paintbrush and allow it to dry. Apply a coat of paint to the area that matches the color of the rest of the jamb.