For more information about snapping existing game objects, see Moving Objects.
To snap a game object to the surface of another:
To snap a game object to a vertex of another object:
To rotate the moving object so that its Up axis is parallel to the normal axis of the target object when it snaps to a vertex, before snapping the object to the vertex of another object, select the Modify > RotateOnSnap menu item to turn Rotate on Snap on.