1) Trapping laws vary by county. They are typically quite intricate. An SAS survival guide will be of no use here. For that matter, most of the traps on the link above are illegal in the US. (For real survival situations, see (3) below.)

2) You'll need a valid hunting/trapping license.

3) And finally, purposefully putting yourself into a situation where it would be reasonably expected that you'll be forced to violate laws for your own survival is not a defense.

In other words, going into the woods without food or the licenses to obtain it sounds like you're all set to break the law. Claiming you "had to" because you decided not to bring any food with you isn't likely to get you very far.