2 main ways - use whichever is appropriate.
Hierarchy Panel > Affect Pivot Only, then (in the Perspective viewport) :-
If you need corners or edges (centers of them) then the easiest would be to use the Snaps either to Vertex or Mid Point.
For faces it's not so easy because a Face is a Triangle (even on a quad poly - 2 triangles) so I would use Center to Object (same panel as affect pivot only) then use the Align Tool (main toolbar) Z axis only, Current = Pivot Point, Target = Maximum (for the top) or Minimum (for the bottom). Select just Y or X axis for front/back or sideways.
Between the 2 methods you should be able to accurately place the pivot where you need it.
If it's an irregular object then it's going to be more difficult to place it accurately - the center may not be quite where you expect it to be. Also note that the current Coordinate System (View, World, Local etc) does have an impact.
Max 2016 (SP1/EXT1)
Win7Pro x64 (SP1). i5-3570K @ 4.4GHz, 8Gb Ram, DX11.
nVidia GTX760 (2GB) (Driver 430.86).