As Barrie says, yes, they are one of the great riches of English. But that doesn't make them any easier to learn. Phrasal verbs are part of what English has instead of perfect tenses and subjunctive moods and ablative cases and dual numbers and like that: namely, syntax.
Since English speakers have lost all that stuff, we have to use syntactic crutches like
- auxiliary verb constructions (She will have been photographed by then)
- determiner phrases (Quite a few of the girls were there tonight)
- reduced relative clauses (The man standing there is the one from the office)
- reduced complement clauses (He believes this bill essential to his constituents)
- enclitic prepositions of several varieties:
- transitivizers (sleep in, look at, listen to, think of 'recall' ~ think about
- idiomatic & metaphoric combinations (look out for danger, go up against him)
- phrasal verbs proper, with stress on particle (look it up, turn down the offer)
- and transitive phrasal verbs, with particle shift (look up the book ~ look the book up)
The easiest thing to do is to get a good dictionary of phrasal verbs, and learn a little about their syntax. It may seem strange, but it comes in handy in recognizing and using them.
As for when it is appropriate to use them, treat every phrasal verb as if it were a separate verb, not necessarily related to its root verb; it's just vocabulary. Then, just as you would with any verb, listen to the conversation and talk like the people you're talking to. If they use them, you can; if they don't, don't.
That's assuming these people already know what's appropriate. If that's not the case, then make it up for yourself; that's what everybody else does.