To repair a bay window that is leaking, cover the caulking on the window with masking tape, making sure to leave about 1/4 inch between the tape strips. Squeeze out a line of caulk about 1/4 inch in diameter, and lay it onto the space between tape strips. Use the bottom side of an old spoon to make the surface of the caulking look smooth and finished. Peel the tape off right away, before the caulking dries.
To repair a damaged bay window sill, inspect the damage. You can only repair sills if the damage goes into the wood no deeper than 1/4 inch. Otherwise, the sill needs to be replaced completely. Use a hand sander to smooth out the surface of the window sill. Be careful when turning the sander on, making sure that the sander isn't touching the surface of the wood. Turn it on to a slow setting, and carefully lower it onto the wood.
Continue sanding the surface until there is no more damaged wood left. After that, use a fine-grit sanding block to prepare the surface for paint or stain. Coat the wood with the stain or paint of your choice, allow the material to dry completely and apply a coat of clear polyurethane sealer to make sure that the wood doesn't get damaged by water again.