Determine what you want to do to the floor after you have removed the old carpet. Do you want to refinish the hardwood and leave it bare or cover it with a new carpet?
If you are removing the carpet as part of a remodeling that includes painting the walls, do the painting before removing the carpet. That way you can dispose of any painting mess at the same time you throw out your old carpet.
Clear the room of everything.
Remove the baseboards or at least the quarter-round at the bottom of the baseboards. This allows you access to the carpet edge.
Carpet is held in place by two methods. Wall-to-wall carpeting is usually held in place by tack strips. These are pieces of wood with rows of tacks driven through them. The tacks face up and the carpet is stretched over them and the tacks hold the carpet in place. Alternatively, carpets can be held in place with glue.
Start in a corner and try pulling the carpet up off the tack strip. This may be harder than it sounds since the strips hold carpet very firmly. If you can't get the carpet started, try sliding the blade of a screwdriver under the carpet and pry it up. A pair of vice-lock pliers may help you grab the carpet firmly to pull it off the tack strip.
Once you get the carpet started, continue to pull it off the tack strips all around the room.
Use a utility knife to cut the carpet into manageable rows. It's easier to handle the old carpet if you can roll the strips as you remove them.
Carpet that is glued in place is surprisingly easy to remove. You should apply glue only to seams and edges (not all over the floor).
Using a sharp utility knife, cut the carpet from corner to corner. Do this from opposite corners, and you will end up with four large triangular-shaped pieces that meet in a point in the middle of the floor.
Pick up one of the points and peel the carpet back. (It will peel off the glue on the edges of the room.)
Once you have removed the carpet use a chemical solvent specifically designed to remove glue (available at a flooring store or your home store) to soften the glue and then scrape it off the floor.