What can be done to fix a squeak in stairs?
Since the house is 100 years old, the stairs are probably constructed using a tapered groove and wedge system.  The stringers typically had tapered dados cut into them to receive the stair treads.  Wedges were tapped in with glue underneath the tread to lock the tread into place.

Check if this is the case by looking under the stairs.  Hopefully the underside is accessible, if not you might have to remove some drywall or plaster.

If the stairs are constructed using tapered dados, please don't nail or screw the treads in to stop the squeak.  It might work for a year or two, but the treads will expand and contract, loosening the fasteners which will then squeak worse than ever.

Assuming you can get to the underside, find the squeaky stairs.  If the wedges are still there and sound, remove them, clean them, apply glue to the faces and tap them back into place with a hammer, tightening up the stair tread.  If, as is often true, the wedges are missing or splintered/broken, cut a new wedge using an existing wedge as a model.