Inspect the staircase to determine what the problem is. Look for obvious signs of damage that may need to be repaired, such as loose handrail or balusters, loose treads or toe kicks, or the stairs pulling away from the wall.
Go up and down the staircase and listen for squeaks and cracks while looking for any visible damage. Write down the stairs that need to be repaired.
Remove any drywall from underneath the staircase to gain access to the stringer, stair treads, and risers. Cut the drywall in the corners and seams to keep the drywall paper from tearing on the adjacent walls. Use a sharp utility knife for this step. Tear the drywall out and remove any nails or screws that remain in the bottom of the risers. A pry bar and hammer work well for demolition of the drywall.
Look for loose shims and wedges between the stair treads and risers. These can work loose over time and cause squeaks. Apply some polyurethane glue to the shims and knock them back into position. The glue will expand and hold the shims fast and stop the squeak.
Drill a few holes, slightly smaller than your lag bolts, through the stringer and into the wall studs, if the stringer has become detached from the wall. Use an adjustable wrench to screw your lag bolts through the holes you've drilled to pull the stringer back tight against the wall.
Apply wood glue to any loose balusters and let it run into the joint. With a damp rag wipe off any excess glue that may have squeezed out of the joint. Toenail a 11/2-inch finish nail into the tread and through the baluster to keep it in position while the glue sets. Countersink the nail head using a hammer and nail set.
Use screwdriver to tighten any loose screws in the handrail and repeat Step 6 for the top of the baluster and the hand rail.
Replace the drywall under the stairs and use painter's caulk to caulk any loose joints.