You only put an apostrophe in its if you want it to mean it is. So you might write: "It's raining men" or "It's a little too quiet out there".
Otherwise, there is no apostrophe in its. Ever.
"A ladybird can't change its spots." "The flu has run its course." "It's scratching its nose."
I suppose the confusion has arisen because you put an apostrophe before the s when you want to show it belongs to someone. So you'd write "Julia's blog" or "The Queen's English." But just because you'd write "The dragon's fire", it doesn't follow that, if you didn't mention the dragon, you'd write "it's fire". To me, that would mean "It's fire! Run for your life!"
Another way to remember it is that you don't put an apostrophe in his or hers so you don't put one in its if you're talking about something belonging to it.
That's all there is to it. Or its.