Pull the carpet away from one corner using pliers until you can get a good grip with your hands. Continue to pull the carpet away from the tack strip, being careful to keep seams intact, especially around doorways. Since you are restretching an existing carpet, you will leave the tack strip along one full wall and pull up the other three sides.
Use pliers to remove the staples from the padding then pull it back. If you don't remove the staples first, the pad may rip because most of it is made of a foam type of material.
Remove the old tack strips, using the pry bar. The tacks are extremely sharp so a pair of work gloves is a good idea to use here.
Lay the new tack strip in place with the tacks pointing towards the wall and secure them to the floor with nails driven into the pre-set holes. Place the strips without gaps between them, especially at the corners.
Staple the padding back in place. Use a staple every 3 inches and along seams.
Rent a power carpet stretcher and knee kicker if you don't own them. It's probably a good idea to ask a friend to help at this point. If you have never used a power carpet stretcher, have someone at the rental company give you a run down on how it works.
Start power stretching, beginning at the center of the wall that has the carpet that you left attached to the tack strip. Stretch a section then move over 18 inches and stretch another section, each time pulling the carpet and hooking it onto the tack strip. Continue in this manner, first working your way towards the side of the room that has a door. Then repeat on the other side, starting in the middle and working your way out as before.
Stretch the sides. This time you only need to start about a foot away from where you pulled back the carpet. Stretch and hook the carpet onto the tack board in the same manner as before and then stretch and secure the other side.
Use the knee kicker in areas that are hard to get to, such as corners and around built in cabinets. Sink the teeth into the carpet about 6 inches from the wall and use your knee to push the tool and stretch the carpet towards the tack strip. Grip the edge of the carpet and pull it onto the tacks as before.
Run the carpet cutter along the baseboards and cut the carpet side, leaving the backing intact. Use the utility knife to trim around corners and built-ins, then cut the backing and leave about 1/8-inch carpet overhang to tuck under the baseboards.
Finish your carpet-restretching job by pushing the edge of the carpet into the tack strip and under the baseboards. A screwdriver and hammer will do the job, but a quicker way is to use the carpet cutter. You won't be cutting the carpet, just forcing the front edge of the carpet cutter into the carpet and dragging it along the wall. This will mash the carpet into the tack strip and force it underneath the baseboards in one movement.