“His”, “Hers” and “Its” have no apostrophe.
“He’s”, “She’s” and “It’s” do.
So to help decide where to put the apostrophe, personify the pronoun. If you have a sentence like “It’s going to shed its skin”, use “He’s going to shed his skin”. It’s best to use the male form to keep the trailing “s”, because “Hers” is incorrect in places where “Her” should be used instead.
Using an apostrophe to save the effort of writing a little “i” hardly seems worth all the confusion. But that’s the way it is.
BnmnG 