Do I need one? And if so, where?
Apostrophes do two distinct jobs: they take the place of omitted letters, as in it’s for it is and don’t for do not; and they show that a noun is being used possessively, such as in a children’s book or the Obamas’ dog Bo.
Apostrophes don’t belong in possessive pronouns, like its, as in The dog licked its lips (does it mean it is? If not, no apostrophe!), hers, ours, etc., or in ordinary plural nouns that end in s, like He owns a lot of hotel’s (no—it’s hotels), or The gatecrashers greeted the Obama’s warmly (no—they’re the Obamas)!
And that’s (that is!) that. Easy.