Make several cuts into the carpet padding using a utility knife. These cuts will allow you to more easily pry up the padding with your putty knife and will allow water to seap through to the glue. Try not to cut into the concrete underneath the carpet. Wear gloves, eye goggles and an apron to protect your hands, eyes and clothes.
Pour some boiling hot water on the carpet padding. Let the water stand for a few minutes and soak into the padding and adhesive underneath.
Pry the padding up using a putty knife. Cut the padding into strips with your utility knife, and place the strips in a trash can. Continue until all the padding has been removed.
Start scrapping the adhesive from the concrete floor with a putty knife dipped in boiling hot water.
Apply an adhesive remover to any spots where there is a heavy buildup of adhesive. Scrap up any remaining adhesive.
Sweep the concrete floor, and then mop with boiling hot water. Let it dry before installing the new flooring.