If you have a house that was built before the advent of pressure-treated lumber, you may have rotten sill plates. Sill plates are pieces of wood that are placed around the perimeter of a building to rest the walls on. The sill plate is sandwiched between the concrete of the foundation and the bottom plate of the wall. Because of the wicking properties of concrete and masonry, untreated lumber that is in contact with these materials for a long time is subject to rot.
Remove the siding from the bottom of the outside walls to expose the sill plates. Pry off the siding with a claw hammer or crowbar.
Cut any anchor bolts that are holding the sill plate in place by running the blade of a Sawzall along the crack between the sill plate and the concrete below it. Work the saw along until you hit something that slows it down. This is probably an anchor bolt. Cut through it.
Cut through any nails and screws that are holding the sill plate to the bottom plate of the wall by running a Sawzall along the crack between these two components, cutting through whatever the saw blade comes into contact with.
Cut some holes through the interior drywall at the top of the first floor to expose the top plate of the wall using a utility knife. Install a temporary jack post from the floor up to the underside of the top plate.
Turn the thread of the jack post with an adjustable wrench to lift the wall just slightly. You will probably hear creaks, groans and pops. Don't overdo it.
Support the wall every 4 feet with a jack post installed against the top plate. If you don't have enough jack posts, put a temporary beam in the location of an installed jack post, then use the jack post in the next location.
Remove the rotten sill plate once you have the wall properly supported.
Replace the rotten sill plate with a pressure treated sill plate of the same dimensions.
Secure the new sill plate by driving 3-inch-long Tapcon concrete screws through the sill plate and into the foundation wall. You will need to drill a pilot hole with a hammer drill to get the Tapcons into the concrete.
Reverse all of the preparatory steps you completed. Loosen the jack posts, allowing the wall to rest on the new sill plate. Remove the temporary beams and jack posts. Patch the interior drywall and replace the exterior siding.