When measuring the distance between two objects to find universal gravitation where must you measure from?

The distance is measured between the 'centers of mass',
or 'centers of gravity' of both objects.  That's the point inside
the object where there's the same amount of mass in every
direction away from it.

If the object is something like a sphere, or a cube, or a uniform
wooden board, or anything "symmetrical", then the center of mass /
center of gravity is the actual center of the object.  If the object has
some irregular shape, then it's harder to calculate or measure where
its center is.