"sid" wrote:

If I finish my basement and start by placing insulation foam board
against the basement walls, which way should the foil face?

Inside, if there's only 1 and no airspace between the board and the wall.
That way, the foil adds about R2 to the board insulation value. The board
itself is a vapor barrier, so from that point of view it doesn't matter
where the foil goes.

Double-foil board will work better with an air gap between the foil and
the wall, but the wall foil needs another vapor barrier on the wall itself
(eg polyethylene film) to protect the foil from moisture.

Nick