Locate any bumps or lumps on your concrete floor and chisel them off as clean as possible using your cold chisel and hammer. Wear safety glasses, as concrete bits can fly everywhere while you chisel and hammer away.
Fill in any deep spots or valleys with a light skimming of thinset mortar. Use the flat end of your thinset and apply a second layer if the first doesn't fill the depressions completely.
Lay tack strip around the entire perimeter of your room, cutting any corners or short pieces with tin snips. For newly-constructed rooms, leave 1/4 inch between the tack strip and the wall. If a baseboard is already in place, leave 1/4 inch from the baseboard.
Hammer your tack strips in place. You'll need to avoid tapping them into place, making sure you give them a good pounding so they affix to the concrete.
Roll out your padding, which should be cut to fit just up to the edge of your tack strips. If seams exist, especially where you had to cut the padding to make it fit into a difficult spot or small nook, connect the two pieces with thick, clear plastic tape.
Lay your carpet down, leaving 1/2-inch over the tack strip around the perimeter of the room. If you have to cut the carpet to get it to fit into tight spots, apply some carpet tape to bring the two sides together and seal it seamlessly with a carpet iron.
Start in one corner of the room and, using your knee kicker, pull the carpet in the direction of the wall and attach it gently to the tack strip.
Trim off the excess carpet with your carpet trimmer, making sure to leave between 1/2 inch and 3/4 inch of a lip up against the walls.
Secure the lip of carpet to the tack strip using a putty knife to wedge it between the baseboard/wall and the tack strip. Be careful not to hammer down on the nails, as they bend easily.
Work your way around the room, either clockwise or counterclockwise, repeating Steps 3 through 5. Be certain to eliminate any wrinkles or loose spots in the carpet as you go.