Use your hand saw to cut your tackless strips to fit each angle of the doorway. Install tackless strips around the edge of the door frame using your hammer and nails. Place each strip about 1/2 inch from the edge of the wall and the door frame. Do not lay tackless strips across the doorway opening. They will cause unwelcome lumps in the carpet, which will in turn prevent the door from closing properly.
Lay carpet padding throughout the room, so that it edges right against the tackless strips. Lay the padding onto the floor, and use your carpet knife to trim it to fit. Use your stapler to fasten the padding to the sub floor. Cover the seams between your carpet padding with Duct Tape to prevent movement and tears.
Lay your carpet over the padding, and over the tackless strips along the edge of your doorway opening. With the carpet overlapping the strips about 4 to 6 inches, use your knee kicker to set the carpet in place on the tackless strips. Place the knee kicker at one corner of the door opening, and while pressing the carpet down with your hands, use one knee to strike the knee kicker, which will in turn hook the carpet onto the tacks, while ensuring that it is taught.
Move the knee kicker to the next portion of the door joint and repeat the process. This may require that you place the knee kicker at several angles in order to set all of the carpet onto the corresponding tackless strips. Each time you finish setting the carpet on one door joint edge, use your stair chisel to press it firmly into position, and ensure that the tackless hooks are set in the carpet backing. Run the chisel along the edge of the wall, pressing down and inward toward the wall.
Cut along the edge of your carpet around the door joints. Use your carpet edger to cut the straight portions, and use a carpet knife and putty spatula to cut the tighter angles and short sides. To cut straight lines, make a 3-inch long diagonal slice in the carpet with your knife. Slide your carpet edger into the slice, and run it along the edge of the wall. The excess carpet will be cut away, and just the right amount of carpet will be left.
Fit the carpet to each corner of the door joint. Use your carpet knife to cut a slit straight downward, into the carpet, in line with the corner bead. This will create two flaps of carpet. With outside corners, lay one flap on each side of the corner, and use your carpet knife to trim it to fit. With inside corners, press the center of the slit down to the floor so the two flaps are elevated along each wall. Use your carpet knife to trim to fit.
Use your carpet knife blade to press the carpet edges under your wall and door jamb molding. Use your carpet knife to cut the carpet at the center line of the doorway opening. Install a saddle over the carpet edge to create a smooth transition into the next room and its flooring material.