Patching holes in a wooden dog house depends on how big the hole is.  If it's a small hole (less than 1/2 inch diameter), go ahead and buy some wood filler and use a putty knife to flatten the surface.  If the wood hole is large, then you'll either have to use wood glue and a piece of wood to patch the hole.  Alternatively, you can use nails to screw the wood around the hole.