There are several reasons why stairs develop annoying squeaks and creaks. The incorrect use and positioning of screws is always a possibility and in some cases the problem could be caused by an adjacent structure. If the two are not anchored securely one to the other, then creaking will be caused.
But probably the most common cause is the fact the holding blocks, which should have been glued and screwed into the top and back of the riser and the front and underside of the tread, have moved or become loosened. Similarly, the fault could be the fact that the wedges used to strengthen the stairs by being inserted between the stringer and the blocks have also become loose.
The method of repair depends on whether or not it is possible to gain access to the underside of the full length of the staircase.
If this can be done check the holding blocks and, if they are loose, they must be re-glued and reinforced with new screws. If damaged, they should be replaced. If the wedges have become loose, tap them firmly back into position and glue them in place.
When access is not possible, start by removing the stair covering. Drill pilot holes into the front edge of the tread where it is immediately above the top edge of the riser. Good quality countersunk screws should then be driven home to tighten down the affected areas. Fill in the screw heads with filler and replace the stair covering.