Measure out the area of the floor to be covered. Leave an inch of space around the edges of the room to allow for nail strips.
Choose a carpet padding that is as thick as the carpet that you plan to install. Choices include Rebond, frothed foam or slab rubber.
Sweep and vacuum the floor to remove any grit that might keep the tape from sticking to the concrete.
Lay down a grid of double-sided carpet tape to hold the padding in place on the concrete floor. Keep the strips of tape about 3 feet apart so that you can pull up the padding without too much difficulty later.
Glue down the nail strips or tack strips with a strong constructions adhesive around the perimeter of the room, making sure that the nails are pointing toward the wall. Let the glue dry overnight before attempting to install the carpet.
Lay the carpet over the padding. Use a utility knife with new blades to cut the carpet around the edges of the room. Use a knee carpet stretcher to stretch the carpet over the nail strips. Connect any seams with carpet tape following the manufacturer's instructions.