Its' is always wrong.   There is no such word as its'.

It's is a contraction for it is.   You can always use it is instead of it's.  They are pretty much interchangeable.

(Note:  Some instructors don't accept contractions in formal papers, as contractions are not recommended by the Modern Language Association.)

It's thundering outside.
It is thundering outside.

It's sunny outside.
It is sunny outside.

It's quality that counts and not quantity.
It is quality that counts and not quantity.

Its

When my son was in grade school he used to misuse  the word its.   I explained to him that its is a possessive word, etc., but he still came home with errors.

One day, I finally got through to him.  I tried a simpler explanation. He grasped the concept immediately. 

I told him that whenever he hears the its sound, if he can substitute  it is for that sound, then he needs it's.

If he can somewhat substitute his or her for the its sound, then he needs its.  Although the his or her substitute is not an exact match, it's pretty close.   His, her and its  are all possessive pronouns indicating possession.

The alien wiggled its eyes.
The alien wiggled his eyes. (close match)
The alien wiggled her eyes.(close match)
The alien wiggled it is eyes. (not acceptable)

What is its top speed?
What is his top speed?  (close match)
What is her top speed? (close match)
What is it is top speed  (not acceptable)

The unicorn bumped its horn.
The unicorn bumped his horn. (close match)
The unicorn bumped her horn. (close match)
The unicorn bumped it is horn  (not acceptable)

This is its new  monitor.
This is his new  monitor.
This is her new  monitor.
This is it is monitor (not an  acceptable substitute)

It's is also a contraction for it has

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It's been a bad day!
I'm sick with a headache & temp.