Pry the original brick mold from the door frame with a hammer and pry bar at the top and down both sides. Pull any nails that remain with locking pliers and scrape old glue, caulking and other debris from the face of the door jamb and the edge of the brick to provide a clean installation area.
Use the original brick mold as a template. Mark the new pieces to the same length and cut the top corners of each side, and both corners of the top piece at 45 degrees with a miter saw. Position the side pieces first, pressing them out to the edge of the brick. Nail through the inside edge of the molding with 2-inch nails from a pneumatic finish nailer, one every 8 inches. Do this on both sides.
Fit the top piece of brick molding so that its ends match up with the top ends of the side pieces. Nail through the lower edge into the top of the door frame, one nail every 8 inches.
Fit a tube of painter's caulk into your caulking gun, tip down. Cut the end of the tip and poke a wire up inside the nozzle to pierce the foil. Pull the trigger to engage the plunger and press the caulking from the tube. Drag the nozzle on a 45-degree angle along every seam to fill it. Fill the nail holes with caulking. Smooth the caulk into place with a dampened finger.
Apply two coats of latex paint to seal the brick mold. Use a fine bristle brush and apply the paint in line with the grain. Spread it evenly to prevent runs and drips. Allow the first coat to dry for one hour before applying the second coat.