Apply the skin. You can use hot glue or spray adhesive. The latter provides a stronger bond, but is harder to work with. Cut a piece of fleece that is big enough to cover your puppet head and start gluing it to the middle of the face. Make sure you glue the fleece deep into the eye sockets. Moving out from the center, keep readjusting, stretching and gluing until you have cover the face evenly and securely. Be sure to leave some extra for the neck.
If you cut off the nose earlier, apply the nose after you put the skin on. Cover the nose with fleece after you apply it.
Use the fleece to hold the jaw onto the face.