Remove the wallboard or paneling, with the pry bar, on the wall with the water damage. It may be best to remove all of the wall covering so a thorough inspection of the cavity can be performed. A full stud count can be done along with the visual inspection for mold.
Test each wall stud for soundness by placing a blow from the hammer to the stud. Perform this along the vertical length of the stud. If any signs of deep depression result from the blows, mark this stud for replacement. The stud may also be retaining water. If the stud seeps moisture after the hammer blow, it, too, may be a candidate for replacement.
Cut a replacement stud in half with the saw. Lay these two halves on the floor to either side of the stud being replaced. Place two full-length replacement studs to either side of the stud being replaced in a vertical position. Wedge these studs between the half plates laying on the floor and the top plate of the wall cavity. The purpose of these two studs is to take the load bearing weight of the wall while the damaged stud is removed.
Measure the actual length of the stud by measuring between the bottom and top plates next to the stud. There may be a slight length variation of the existing stud and the replacement. If so, mark the length on the new stud with the pencil and cut to length with the circular saw.
Remove the damaged stud. Pull or bend over the exiting nails in the top and bottom plate. Insert the replacement stud into the wall cavity. Check the center spacing with the tape measure.
Drive two 16 p nails through the new stud into the bottom plate. One from each side. Perform the same task to the upper plate. Remove the support studs from either side of the new replacement. Move to the next damaged stud. Repeat until all studs are replaced.