Its and It's are totally different from each other. Its denotes possession. For example:
The dog wiggled its tail.
It's is a contraction of it is and in other cases, it has. For example:
It's the responsibility of the parents to educate their children. (It is the responsibility of the parents to educate their children.)
It's been said that life is good when you are laughing. (It has been said that life is good when you are laughing.)
You can read this article (http://www.slideshare.net/stephlowe91/ielts-grammar-training-rules-in-using-apostrophe) to educate yourself on the proper use of apostrophes (rules).
is - it is a linking verb that connects the subject to its complement. For example:
Jack is going to visit his father's grave today.