I've been wondering about feats: many of them, like Toughness, are "passive", so they are always working and PCs are always enjoying their benefits. Others, instead, like Power attack or Cleave, need to be declared before attempting to roll the dice. Is this difference actually present in Pathfinder, and if so, there are any special rules (sorry for such a generalization but I can't be more precise) that regulate them?
For example, my greatest doubt is about how many feats can I declare before attacking: can I, at the same time, use Power Attack, Vital Strike and then also Greater Cleave on the same enemy (and of course to all the other surrounding it)? Or I have to just choose between one of them, because just one "active" feat can be used per turn?
I've repeatedly searched the Core Rulebook but I haven't found anything about this. So is such a rule about feats just absent (and thus I can use as many feats as I want) or is it implied somewhere, or maybe I just missed it?