Most staircase problems revolve around loose handrail systems. Handrails rely on newel posts -- the large anchor post at the bottom and top of staircases -- for stability. When the newel post gets loose it can cause a chain reaction that loosens the entire handrail system. Most repair manuals say you can simply screw the newel posts back down, but this is only a temporary fix that will come loose later. To properly fix it you need to get back to basics by using wood, glue and clamps.
Measure 5 cm (2 inches) up from the bottom of the loose newel post on the side and mark it. Take your 3 mm (1/8 inch) drill bit and drill down at an angle just above your mark through the bottom of the newel post as deep as your drill bit will allow, tapping into the stair tread.
Using your 1.8 cm (3/4 inch) Forstner bit, place the tip into the pilot hole parallel to the newel post and begin drilling. After the bit has sunk 6 mm (1/4 inch) into the post, tilt up the drill and follow your original 3 mm (1/8 inch) pilot hole as deep as your bit will allow.
Clean out the debris and wood chips. Measure with a pencil and cut your 1.8 cm (3/4 inch) dowel 2.5 cm (1 inch) longer than the depth of the hole. Place masking tape around the base of the newel post to prevent excess glue from getting on carpets, etc. Test fit the 1.8 (3/4 inch) dowel with fingers only -- do not hammer it in yet.
Squirt glue into the hole, spreading it around inside the hole with your pencil. When the hole is completely saturated with glue, hammer the dowel into the hole until it bottoms out.
Place one bar clamp from the front of the newel post to the next post in line near the bottom, and one in the middle. Place your level on the newel post, and tighten your clamps. Let it dry overnight.
Saw the remainder of the dowel off flush with the newel post and putty the edges. After it dries, sand and stain it to match the post.
Check all the joints in the stair system. Glue and clamp those as well if needed. Make sure you use the Forstner type drill bit -- it's the only kind of bit that cuts cleanly.
Check before you drill for any nails or screws that might be in the way. Do not fill the hole with glue. It will create a hydraulic affect and split the newel post.