There are a variety of ways to repair wainscoting in your home, depending on the level and type of damage. Wainscoting, which is wood paneling applied to a wall from the chair rail to the floor, is a feature more commonly found in older homes. It was originally installed to protect walls from moisture damage but has now become more of a decorative addition.
If your wainscoting has only surface scratches or gouges then the repair is simply to fill them in with wood putty. Clean off any excess and allow it to dry. Then brush over the repairs with a matching wood stain and allow it to dry and the damage will disappear. Very light scratches do not even require putty. The stain will be sufficient to repair them.
Now if you wainscoting is cracked or seriously damaged, you will have to remove the damaged section and replace it with new wood. Purchase a matching section and bring it into the house. Allow it to sit for several days before installation. It will absorb the normal moisture in your home and expand. Pry off the chair rail above the old section and remove all the nails. Using a keyhole saw, cut out the damaged section of wainscoting and remove it from the wall. Use a crowbar to pry it off of the wall. Remove all nails and thoroughly clean the wall underneath. You may have to use a hacksaw to cut the nails attaching the wainscoting to the baseboard.
Nest, measure the open section and, using a circular saw, cut the new wainscoting to match the dimensions of the open section. Nail the new section into place on the top and the bottom. Now take the chair rail section that you removed earlier and attach it back into place. Cover the exposed nail heads with wood putty. Stain the new wainscoting to match the original and you are finished.