Keith has a good strategy but I feel compelled to copyedit the presentation a bit:
"The bird used its wings" is right because it could be "The bird used his wings" and that would still be an English sentence.
"The bird used it's wings" is wrong because it could not be "The bird used it is wings" - that is not even English.
"It's time for bed" is right because it could be "It is time for bed."
"Its time for bed" is wrong, because "His time for bed" is no longer an English sentence.
I think there may be cases where you'll feel it is awkward to substitute another posessive pronoun for "its" so that test might not work all the time. But if you can substitute "it is", you can be sure you need the apostrophe.
By the way, it might help to realize that there is no logic to this, the language is just fuck*ng with you. In other cases you need the apostrophe to make a possessive, like "Wombat's pugs," whereas in this case you have to leave it out. It doesn't make sense, it's just a way for a guy like the one in my link to screen resumes, basically. So don't try to make sense of it, just memorize the tests for which one to use.