IMO, the best way to learn intuitive F2L... is by algorithm F2L.
Sounds weird, I know, but that's how I learned it (in like a few days) without memorizing any algorithms (almost).
http://www.cosine-systems.com/cubestation/cs2/3x3x3/cfop/f2l/f2lprintablepage1.php
http://www.cosine-systems.com/cubestation/cs2/3x3x3/cfop/f2l/f2lprintablepage2.php
Just print it out, and look for a specific case, and instead of memorizing it, analyze how it works. It should be easy enough (except for algs that "destroy the cross, move the cross edge piece around in the U layer, and magically form it again"... just memo the alg in that case or find your own solution). Soon enough you'll understand it enough that you won't need the guide anymore.
This way is best IMO, because it prevents you from creating F2L "solutions" that make many wasted unnecessary moves. i.e. it keeps your move count down.