Work from under the floor in the basement or crawlspace in the approximate location of the squeak. Have your helper step or jump where the squeak occurs on the floor above. Observe the subfloor and joists, looking for movement.
If you locate a gap between the subflooring and joist, use a pair of shims to provide support. Push the shims into place from both sides of the joist. Insert just enough shim to fill the gap without lifting the subflooring, which creates another gap.
Some gaps are too small for a shim. Use a caulking gun to apply construction adhesive to the gap. Push as much adhesive as possible into the gap from both sides without lifting the flooring.
If the floor joist itself has suffered damage, nail a second board to its side for additional support. Choose the same dimension lumber as the existing joist. Cut to a length that allows nailing the sleeper into the undamaged portion of the existing joist. Shim the floor as needed to provide support.