Take photos of both sides, print them out *large*.
Any connections you can't work out quickly from the pics, meter out.
A graphics package will help as you can flood fill tracks or PCB, alter contrast, change colour depth etc to make tracks stand out (though some PCB coatings make it damn difficult)
Helps if you can identify ICs, devices etc. as there's only so many ways you can connect the majority of non programmable devices and you can quickly identify then ignore power rails until you decide to make a new PCB.
If you can sacrifice a board then as you say, stripping the board is very helpful, you can, after careful photography, then sand it lightly to remove solder masks and expose tracks, vias etc. which makes it much easier to trace out.