I use this method A LOT:
1) Select the object you want to move points from.
2) Select “point select” mode.
3) Select a point on the object you want to move.
4) Under the “utilities” tab, select “Snap/Align”; a little target circle will appear as your cursor.
5) Move the target near the selected point and press your shift key. The target will snap onto the selected point.
6) Drag the point to any other point in the scene, and it will snap to that point as it gets near.
Repeat 3-6 to your heart’s content for any other points you want to snap.
This works from any object to the same or any other object in your scene.