Rent the carpet-stretching tools. As these tools are needed for just a few hours, you needn't purchase them. Visit a good tool rental store and rent a 'power stretcher', 'knee kicker', and a carpet cutter if you do not have one. Purchase a heavy-duty stapler with 5/16-inch staples, if you don't have a set.
Cut and install tack strips. Use tin snips or a chisel to cut the tack strips to the lengths required. Nail down the tack strips along the perimeter of the room, keeping a space ("galley") of about 3/8-inches between the baseboard and the tack strips when doing so. Then staple down the carpet pad along the seams and tack strips.
Attach one end of the carpet to one section of the tack strips, starting from one corner of the room. Allow 1" to 2" of the trimmed carpet edge to overlap the tack strips.
Set the toothed end of the knee kicker about 1" from the tack strips. Firmly embed the teeth of the knee kicker into one section of the carpet edge. Then use your knee to exert pressure on the padded section of the knee kicker. This will move the carpet forward allowing it to be hooked firmly to the tack strips. Repeat this process along sections of the installed tack strips as you work your way around the room.
Place the bottom (toothed) part of the power stretcher about 5" to 6" away from the wall, directly across from the section of carpet attached to the knee kicker. Then use the lever provided to press the teeth of the power stretcher into the carpet and lock into place. Make sure that one end of this unit is attached firmly to the opposite wall.
Gradually stretch taut the carpet until it can be hooked onto the tack strips. Repeat this process around the room until all wrinkles have been eliminated. Use the knee kicker alternately when or where necessary.
Trim all excess lengths of carpeting. Use a carpet cutter, adjusted to the thickness of your carpet, to trim the extra lengths of carpet between the walls and the tack strips. Then tuck all trimmed edges of the carpet under the baseboard trim using a smooth or round-edged plastic ladle.
Remove tack strips. Start removing one section of tack strips at a time while gently tugging to free the carpet. Use a pry bar to remove the setting nails of the tack strips, and a set of pliers to remove all staples fixed earlier to the carpet pad.