WordVale
Textbooks group phrasal verbs by verb: every get together, every take together. That is the arrangement that maximises confusion, because get up, get over and get by have nothing to do with one another. Group them by particle instead and a pattern appears.
UP — completion, or increase
Up usually means something is finished or intensified. Use up (consume entirely), wrap up (finish), speed up, bring up (raise a topic — or raise a child), show up (arrive).
"We used up the milk" is stronger than "we used the milk" — the up is what says none is left.
OUT — thoroughly, or to the end
Figure out (work out completely), sort out (resolve), wear out (exhaust), find out (discover), run out (exhaust supply).
Compare work with work out: the second implies you reached an answer.
OFF — separation, or cancellation
Call off (cancel), put off (postpone), take off (remove, or depart), set off (begin a journey), lay off (dismiss).
ON — continuation
Carry on, hold on (wait), get on with (continue, or have a good relationship with), count on (rely).
The ones that fit no pattern
Being honest: the particle logic is a tendency, not a rule, and some of the most common phrasal verbs are simply idioms you have to meet.
- Put up with — tolerate. Three words, no relationship to putting or up.
- Come across — find by chance, or give an impression. Two unrelated meanings.
- Get over — recover from.
- Look forward to — anticipate happily. Followed by -ing, never the infinitive: "look forward to seeing you", never "to see you".
Separable or not
"Pick it up" is right; "pick up it" is wrong. But "get over it" is right and "get it over" is wrong. Whether the object can sit in the middle isn't derivable from a rule — your ear learns it from examples, which is another argument for meeting these in sentences rather than in lists.
The full hundred, each with its own page, are here, and the method for making them stick is here.