Remove the old covering over the soft spot to reveal the damaged area. Roll the carpet out of the room, there is no need to cut it. If vinyl tile is to be removed, you will have to find new tiles, as they will be damaged in the excavation process and cannot be put back again.
Identify the joints between the underlying layer of the board. There will be a line of nails or wooden screws in the underlying particle layer which will indicate where these joints are. Use pencil and ruler to mark the area of the board damaged by moisture. Inspect whether the damage has been spread to other boards or only piece has been damaged. The area to be removed has to be 6 inches wide on each side of the soft spot. As the plywood has to be screwed at the joints, either one board or two boards will be replaced, there is no other alternate.
Use a circular saw to cut through the joint. You can also use the back side of the hammer to take out the old nails first, if they are easily detachable. Cut the old board frame along the line that you have marked with the pencil. Clean the area with an air blower, and add an insulation agent under the surface before installing the new board.
Either use the old joints or make new one from the 2 by 4 inch boards of plywood. Use a nail gun to fire nails into the plywood to fix the board properly. Attach supporting joints to the old joints with the help of a drill machine and screws.
Apply a paste of construction adhesive over each joint, and fix plywood in its place with the help of the binding agent. Roll back the carpet to finish the small project.