It's always means it is or it has. Its shows something belongs to it. Swap in it is: if the sentence still works, use the apostrophe.
The dog wagged its tail versus It's cold today. The tail belongs to the dog; the second is simply it is. The swap test leaves no overlap: every sentence takes exactly one form.
Here is a simple test for every example below. If it is or it has fits naturally in the slot, it's with an apostrophe is the right choice. If the swap fails, the word is doing the possessive job, so write its, the plain possessive form.
The dog wagged its tail. No swap possible, since it is tail is nonsense. The tail belongs to the dog.
It's cold today. The swap fits perfectly: it is cold today. Nothing is being possessed, so the apostrophe goes in.
The committee has its reasons. The reasons belong to the committee. Reading it is reasons aloud, you hear the break immediately.
It's already been approved. Swap in it has: it has already been approved. The apostrophe marks the missing letters.
One email scene, two jobs: The team met its goal. The goal belongs to the team. It's time to celebrate. That's it is time. Both are correct; the slot decides.
When the sentence starts with Its or It's
Sentence starts are where this pair trips writers most. At the front of a sentence, the capital letter makes the plain form Its look wrong, so a stray apostrophe sneaks in. The swap test still settles it, even there.
Compare two openers. Its cover page is missing. Try it is cover page aloud and the sentence collapses, so no apostrophe, capital letter or not. The page belongs to the report.
Now the other side: It's hard to say goodbye. Here it is substitutes cleanly, so the apostrophe belongs. Both forms can open a sentence; only the swap decides which one you need.
One habit covers both cases. Write the sentence out in full first, it is or it has versus the plain possessive, then shorten it. A sentence-start apostrophe stops being a guess and becomes a check you have already passed.