This reminds me of an episode of Mythbusters where the crew set up a bunch of of MacGyver puzzles for the two hosts - pick a lock with a lightbulb filament, develop film with common household chemicals, and signal a helicopter with a tent and camping supplies.

In all seriousness though, Philisophical Materialism and the Scientific Method are probably the most important things; three years ago I bought my first car for a pack of cigarettes, and a $20 Hayes manual. At the time I didn't even know what an alternator was; three months later I'd diagnosed a major electrical problem, and performed an engine swap. The manual helped (obviously), but for the most part it was the knowledge that any mechanical device could be reduced to simple causal patterns which allowed me to do this (incidentally, this is a hobby that I strongly recommend to other LW members - you get to put the scientific method into practice in a hands-on manner, and at the end of it you get a car which is slightly less crappy).

I tend to think that the mere knowledge that flying machines are possible will allow the survivors of WWIII to redevelop the prewar tech within a century.