You can install carpet six different ways from Sunday over concrete. You can glue it down without a pad, you can glue the pad down and glue the carpet to the underpad, you can glue or tape the pad and stretch the carpet over it with tackless strips glued or nailed to the concrete.
Pull up one corner of the carpet and see if there are any tackless strips (see note below). If so, then there's no glue or tape between the carpet and the pad, so it'll just be a matter of pulling the carpet off the strips, cutting it up, rolling up the pieces and carrying it out. Use a utility knife or razor knife.
Pull on the pad and see if there's glue or double sided carpet tape under it. Carpet tape is easy to take up. It'll be harder to get the under pad off if it's glued down. You an buy or rent flooring scrapers to do this with.
Also, pay attention to doorways. There may be a metal molding in the doorways called "naplock" that may be glued or screwed into anchors in the concrete. If it's glued down with construction adhesive, you can either use a heat gun to soften the adhesive and pry the naplock up, or just wreck a cheap 2 inch wood chisel (like a Fuller or a Stanley) to cut it off the concrete.
If you find small "blobs" of black "grease" under the underpad, that's what's left of the black foam chips in old foam chip pads. The best way I know of to clean those off the floor is with a strong solution of laundry detergent in water.
Note below: Yes, the correct word for them is "tackless strip" even though these strips of wood are full of tacks. Before the Roberts Company patented their "tackless strip" (called "Smooth Edge"), carpets were installed by tacking them down with carpet tacks around the perimeter of the room. These wooden strips eliminated the need for carpet tacks, and hence the name "tackless" strip. Nowadays, people call them "tack strips" cuz they don't know the history.
PS: In the first Blues Brothers movie (called "The Blues Brothers"), Jake (John Belushi) avoids arrest by reaching into the glove compartment of the Bluesmobile to retrieve a box of carpet tacks he keeps there. He throws the tacks out the window to puncture the tires of the persuing police cars.
Otherwise obsolete, you can still use carpet tacks for that.
Ya gotta know these things to get your DIY'er armbadge in carpeting.
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