According to FamilyHandyman.com, the best way to cut carpet is to pull about a 3-foot strip off of the floor, fold this section over the carpet that is still secured to the floor and cut the carpet from the back. The best knife to used for this is a sharp utility knife. Be careful not to cut the baseboard or the walls while slicing the carpet.
To start the process of prying the carpet up from the floor, start in the corner, grab the carpet with pliers and pull. Then grab the edge of the carpet and continue to pull it up along the wall.
Once the carpet is cut, it is easiest to roll the 3-foot strips of carpet into rolls in order to carry it out. If there is a concrete subfloor under the carpet, it is likely that large chunks of the carpet will remain stuck to the floor. The best way to remove the remaining carpet is with a floor scraper. On a plywood subfloor, there will be many staples to remove. The easiest way to remove them is with a sharp floor scraper, although they can also be removed individually with a pair of pliers.