I suppose the normal way would be to install the sash in the frame and mark where you want the hinges on the sash and frame, then remove the sash and install the hinges.

the thing is, the way the hinges on the window were when I took it out was ( and don't ask me whose idea this was) they were screwed into the part of the window that sits on the frame..so they are horizontal and mostly invisible when the window is shut. I believe the part of the hinge connected to the sash was screwed onto the outside (visible with window closed). If that makes sense. Maybe I should just patch the wood and do it the way you suggest.

To paraphrase Lou Costello, When I try to imagine the window nothing happens.

This isn't hard...as Renovator said, put the sash in the frame, hold the hinge up to the sash and frame where you want it to be (on the outside of both)...then mark where the screw holes are.

Next, remove the sash from the window, and transfer the locations of the screw holes to the bottom of the sash using a square. How far in the screw holes are, you determine by placing that leaf of the hinge on the bottom of the sash, lining up the holes with the marks you made earlier, and using a pencil to mark the new holes.

If the hinge is mortised into the sash, trace around the outside of it, and remove that wood with a chisel to a depth of the hinge's thickness.

Unless I'm totally off, when the hinge was originally in place, the only visible part from the basement side was the lower leaf on the window frame...so when the window was closed, the hinge had an L-shape profile. My own basement windows are square, and all hinged on the side, but the hinges are totally concealed as they would be on a cabinet with inset doors.

Personally, I'd do the hinges from the top or side instead. The most simple solution for your original question is to just surface mount the hinge on both halves rather than just the bottom.