Start in a corner of the room, pulling up one corner of the old carpet by hand or using pliers. Roll the old carpet up and carry it out of the room.
Roll up the old padding, if matted down or too worn, and carry it out of the room.
Inspect the old carpet tacking. If it is reusable, leave it in place. If the tacking nails are too old and rusted, pull up the old tacking using a pry bar.
Scrape the subfloor if pieces of the old padding are stuck to the floor.
Open the windows and pour bleach on the subfloor if "pet damage" exists -- which are urine stains that have seeped through the carpet into the subfloor. Let the bleach soak into the floor overnight and then mop the floor the following day.
Install new carpet tacking around the edges of the room using a hammer and masonry nails.
Roll out new padding, if needed, and cut to fit inside the perimeters of the carpet tacking with a utility knife.
Measure the room with a tape measure and cut carpet to fit over the tacking, reaching all four walls with a utility knife. Using a knee-kicker, stretch the carpet out in the room over the tacking on every side. Press the carpet onto the tacking with your foot to make it stick. The carpet edges must catch the tacking for the carpet to stay in place.
Cut off excess carpet with a utility knife and discard the pieces. Your room is now re-carpeted.