The possessive form of it is its. No apostrophe.
It’s = It is, or some other contraction, such as it has. Always. Garner should back me up on this. I don’t own Garner, but I have Fowler, who’s probably just as uppity, who says, “Just a reminder that its is the possessive form of it (the cat licked its paws) and that it’s is a shortened form of it is (It’s raining again) or it has (It’s come).”
Wow, I quoted Fowler almost verbatim.
So, if I’m reading your blog, and you say, “The summer has it’s happy moments,” please be aware my brain reads it AND it means, “The summer has it is happy moments.” If you intended that, that’s one thing, but if you’re referring to happy moments that belong to summer, it’s its. It is, I promise. Or, if you’re unsure, just say, “The summer has happy moments.” I always write my way around a rule if I don’t know it.
It’s a weird rule; its tendency to trip people up is historical. It’s annoying me, particularly today, for some reason. Its dark magic has wrested all tolerance from my soul.
I’ll stop before it gets more obnoxious.