Mark the hole's width on both sides of the wall using a pencil and carpenter's square. Cut along the pencil lines with a drywall saw. Pull the drywall, from the floor to the ceiling, off the studs
Insert a reciprocating saw between a wall stud and the bottom plate (the board running horizontally over the floor) and cut through the nails holding the wall stud in place. Twist the wall stud and pull it away from the top plate (the board running horizontally over the wall studs). Repeat this step for each stud in the opening.
Hold a carpenter's square over the bottom plate. Line up the square's edge with what will be the opening's edge. Draw a straight line across the plate. Repeat this step on the opening's other side. If the opening will reach from floor to ceiling, repeat this step with the top plate as well.
Secure the bottom plate to the subfloor with additional nails. Use 2 1/2-inch nails and place them about 2 inches out from the lines you drew in Step 3. They will hold the bottom plate in place while you remove the section in the opening. If you are removing the top plate, add extra nails to that as well.
Cut through the lines you drew on the bottom plate in Step 3 with a reciprocating saw. Pull that section of bottom plate out of the opening. If you are removing the top plate, cut that along the lines you drew in Step 3 and remove it.