Position yourself under the stairs with a flashlight. Have someone walk up and down the stairs and identify the locations where they creak. Mark these locations with a pencil.
Apply a bead of caulking to joints where you can see light coming through. Press the caulking into the joint by running your finger firmly along the bead so it gets pushed into the joint.
Drill pilot holes at 90 degrees to each other through a wood block. Place the block at the joint where the tread (the horizontal part of the step) meets the riser (the vertical part). Screw the block into the tread and the riser. Use screws that are long enough to go into the tread and riser, but not long enough to break through the other side.