Pull up the existing finished floor and set aside for reinstallation if the material is salvageable. You'll need to pull up the linoleum, tile, wood or carpet, as well as the plywood underlayment between the subfloor and finished floor. You may also need to remove the baseboard trim to provide clearance for removing the rest of the floor.
Inspect the subfloor and assess the level of damage. If it is only damaged in a few places, mark these areas with spray paint so you'll know to remove only small sections of the subflooring.
Mark the subfloor with a chalk line to create a square; two sides of the square must be centered on a neighboring joint. Use the existing nail pattern in the subfloor to locate the floor joists.
Adjust the blade of the circular saw to match the thickness of the plywood and then cut the section of plywood out with the saw. Adjusting the blade ensures that you don't cut the joist and compromise the structural integrity of the floor.
Pull the old piece out and pry up any remaining nails from the floor joist with a hammer. From here, install a new piece of subflooring, matching the flooring type and thickness to the original subflooring material.
Locate the seams of the plywood or OSB subfloor if after the inspection you determined that you must replace an entire sheet.
Wedge a pry bar in the seams of the sheet, and then push down on the bar to pry the subfloor from the joists. Move farther down the joint and pry in another area, repeating as needed until the entire board is removed.
Continue removing one sheet at a time if you are replacing the entire floor. Remove the one damaged sheet and replace with a new sheet before moving to another part of the floor; this prevents you from having to replace the floor while balancing on floor joists.