Vacuum your old carpet to prevent breathing in dust and dirt when you rip it up. Use a utility knife to cut the carpet into strips so that it is more manageable to remove. Rip up the strips and expose the carpet padding between the carpet and the floor.
Roll up the padding and throw it away. If your carpet is fairly worn, there is a good chance that the padding will not produce enough of a barrier between the carpet and the floors. Remove any tackless strips.
Clean the floor that was under the old carpet. Make sure that it is free from dust and dry.
Install new tackless strips around half an inch from the wall around the perimeter of the room. Avoid putting the strips under the door, because they will catch.
Install the carpet padding, ensuring that the tackless strips are facing the wall. Cut the padding so it fits the size of the room. Wrap duct tape around the edges of the padding to prevent it from coming undone. Measure the room in order to cut the new carpet.
Cut your carpet, allowing for a 6-inch leeway. The carpet should rest over the sides of the walls. Press the carpet down against the wall, and mark the spot underneath where the new carpet lays next to the wall. Cut underneath with a utility knife.
Lay your carpet. Place a knee kicker, which is a mechanical tool with teeth on one end and butted edge on the other end, with the teeth facing the wall. Make sure that it is 3 inches from the wall. Press against the butted end of the tool to stretch the carpet to the tackless strips. Set two carpet stretchers at either end of the room to stretch the carpet over the tackless strips. Carpet stretchers look like knee kickers, but have an activation lever that you can press when stretching.