Cut off power to the wall you want to remove. The circuit breaker might disconnect power to the entire room; if so, hook up temporary lighting with extension cords from an upper room before turning off the circuit breaker.
Lay drop cloths on the floor next to the wall you are removing. Remove the cover plates from any outlets or light switches with a flat head screwdriver. The junction boxes for outlets and switches attach to the wall studs.
Pry the baseboard away from the wall with a small pry bar and hammer. Once you remove the baseboard, it might be possible to see where the wall studs are located. If not, run a stud finder across the wall and mark the stud locations on the wall with a pencil.
Score through the drywall with a utility knife at the center of each stud. Score lines across the wall and intersect the stud scores every 4 feet up the entire height of the wall. These score lines will help make less of a mess when removing the drywall.
Punch a hole through the drywall in between the studs at one of the horizontal scored marks with the hammer. Once you have a large enough hole to put your hand through, begin pulling the drywall away from the studs by hand.
Remove as much drywall as possible and avoid pulling on any electrical lines. Remove drywall screws from the studs with a cordless screwdriver or drill with a Phillips head bit. It might be necessary to pull the screws out with the hammer or pry bar. This helps remove the remaining pieces of drywall that attach to the studs directly.
Check the area under the stairs for any electrical lines and duct work. Electrical lines should be moved by a qualified electrician. Consider installing a half-wall to cover the side of the staircase if there is duct work present as it is difficult and expensive to move duct work. Before cutting through any studs, determine which ones you want to remove and which ones will stay. Sometimes a small wall at the first few steps is desirable.
Cut the top of the studs even with the ceiling with a reciprocating saw. Ask a helper to hold the cut stud while you cut it where it meets the sill plate on the floor. Do not cut any studs that attach to the bottom of the staircase stringers.
Pry the sill plate off the floor with a crowbar and hammer. The sill is the 2-by-4 inch board that attaches to the floor.