To use it's or its or its': that is the question. And it's a question that commonly confuses many a would-be writer. This is the mistake I see most commonly and glaringly used in government documents, slide shows, and billboards, and one that is so small-seeming that it is frequently skipped over. But it's also a very easy rule to get on top of. Read on and I promise you'll never get it wrong again.
It's: This form is used exclusively as a contraction of 'it is' or 'it has'. When making contractions, the apostrophe takes the place of any missing letters (in this case, the 'i' in is and the 'ha' in has). That's it, folks: only use it's when you really mean it is or it has. Easy trick: read the sentence back to yourself, replacing it's with it is or it has. If the sentence no longer makes sense, you're using the wrong form.
Its: Usually, possessive pronouns are made using apostrophes, as in 'Sarah's boy toy' or 'the man's love of necrophilia'. But not with its. When you are making its possessive, you leave out the apostrophe: 'its weakness' or 'its pumpkin face'. Remember, the apostrophe-using it's is ONLY used when you mean it is or it has.
Its': Its' does not exist. We see it all the time, and we've probably all used it at some point, but there is no such thing as its'. So delete it from your memory bank.