Install tack strips to hold the carpet to the subfloor. Use a tape measure to determine the length needed for the wall, cut the tack strip with a wood saw, and hammer the attached nails into the subfloor.
Use a knee kicker to attach the carpet to the tack strips. A knee kicker is a long metal tool with teeth at one end that grips the carpet and a padded butt at the other end. When you drive your knee into the padded end, the tool stretches the carpet over the tack strip. Lay the kicker on the carpet, with grippers facing the wall, and kick the tool with your knee to stretch and attach the carpet to the tack strips.
Stretch the carpet across the room, using a power stretcher. Place one end of the stretcher at the wall where you used the knee kicker, and pull the other end across the room, adding adjusters for the appropriate length as necessary. Pull the handle to stretch and attach the carpet. Move about 18 inches down the wall, and restretch the carpet. Power stretchers work best in large areas.
Cut all excess carpet from around the wall edges with a utility knife. Use a wide-blade carpet chisel -- shaped like a metal paintbrush -- to push in the carpet edge beneath the baseboards to finish the project.