Read the sentence in question. Wherever you see the contraction "it's," read it as "it is." For example, read the sentence, "The book is not in it's proper place," as "The book is not in it is proper place." Decide if this sentence makes sense. If it doesn't, the use of "it's" is incorrect. Replace it with "its."
Read the sentence in question. Wherever you see the possessive pronoun "its," read it as "its." For example, read the sentence, "The book is not in its proper place," as "The book is not in its proper place." Decide if this sentence makes sense. If it does, the use of "its" is correct.
Ask yourself this question whenever you see or compose a sentence that contains "its" or "it's": "Do I want to say "it is" at this point in my sentence or phrase?" If you answer yes, use the contraction, as in, "It's going to rain tomorrow." If you actually want the possessive pronoun, use "its," as in, "The cat wants its dinner." Using this rule, you'll always be grammatically correct whenever you must choose between "its" and "it's."