If you're confused by these two little words, you've come to the right place. (Not that there aren't other right places.)
It's is a contraction for it is or it has.
Its is a possessive pronoun meaning, more or less, of it or belonging to it.
And there is absolutely, positively, no such word as its'.
If you can replace it[']s in your sentence with it is or it has, then your word is it's; otherwise, your word is its.
Its is the neuter version of his and her. Try plugging her into your sentence where you think its belongs. If the sentence still works grammatically (if not logically) then your word is indeed its.
It's been good to know you. Contraction: it has
The dodo bird is known for its inability to fly. Possessive pronoun: its inability = the dodo bird's inability
See Jack Lynch's popular and handy Grammar and Style Notes.
The Word Detective may surprise you with his history of it's and its.