Stairs creaks because wood is rubbing on wood. Either a
tread or riser is not secure and can be remedied fairly
easily if the under-side of the staircase is accessible.
Under the stairs the ends of the treads are often supported
by wedges. Use a hammer to tighten them by tapping their
ends.
There should be tongued and grooved joints between the
rise and tread sections of each step. Sometimes there are
glued triangular blocks in place, which may need tightening,
or replacing with metal repair plates (or shelf brackets
can be used). It is useful to have someone walking on the
stairs so you can locate where the creaking is.
If the under-side of the stairs is difficult to access
due to decor or plaster covering, then try to remedy from
the front. Locate the position of the creaking and try lubricating
the join with talcum powder or French chalk.
If the treads and risers are not jointed together, gently
prise them apart with a screwdriver and fill the join with
wood glue.
If the treads and risers are jointed, drill and countersink
clearance holes approximately 25cm apart through the tread.
At the top of the riser drill pilot holes in the same positions.
Insert screws into the front of the tread to the riser.
Tighten the screws and cover the heads with filler. If the
stairs are varnished use a coloured filler to match, otherwise
carpet will hide the join. Sand the area for a smooth finish.