Well, you could read SGA. But my two favorite sources for this material are here for an abstract treatment that doesn't (as far as I remember) talk specifically about quasi-coherent sheaves, and here for a considerably longer but readable treatement that does.

(More precisely, the first reference has a section that basically takes various properties of quasi-coherent sheaves as axioms and proceeds from there. If you're willing to accept these axioms without working through all the geometry, that's probably the reference you're looking for.)