modal verb - most common use - sample sentence(s)
can - ability, possibility, permission - "I can sing very well." (and that's true!)
may - permission, possibility - "May I ask you a question?"
might - remote possibility - "If he asks me out I might say yes... I might say no... well, we'll see."
will - a calculated possibility, a spontaneous decision - "I'll probably stay here for the weekend." / "You know what? I'll give you a call tomorrow. How about that?"
Use them to talk about the past (something that happened or didn't happen in the past)
could have done s.th. - hypothetical situation - "I can't believe you drove after all that beer you had. You could have crashed your car!"
should have done s.th. - criticism, regrets - "I failed the test. I should have studied harder."
might have done s.th. - remote possibility - "He didn't come back home last night. He might have slept over at his girlfriend's, or he might have fallen asleep at the bar... who knows?"