For this, the basic rules of thumb are simple:
#1 Never apostrophe before plural-s.
#2 Always apostrophe before possessive-s.
Some weird possible exceptions noted in sibling comments (like apostrophe before plural-s on acronyms and single letters), but those aren't universal and therefore not mandatory. So if in (even the slightest) doubt, follow rules #1 and #2 and you'll be right far more often than wrong.
Oh yeah, one actually important and non-weird "exception": NO apostrophe "before possesive-s" on possessive pronouns like "his" or "theirs". I think this is because they're actually not ordinary nouns made possessive by adding apostrophe-s, but grammatically their own distinct words which happen to always contain an s at the end. So in that perspective, it's not even an exception; hence the quote marks.
And that ("it's") reminds me of rule
#3 Always apostrophe in contractions.
"Contractions" here means when a verb -- usually "is" or "has"; I don't know if (but don't think that) there are any others -- following a noun or a pronoun is reduced to its final 's' and added to the preceding word, as in e.g. "John's gone". You have to figure out whether the 's' stands for "is" or "has" from context: In "John's gone forever" it's "is", but in "John's gone and done it" it's "has". Usually it's pretty obvious, or doesn't really matter for understanding what's meant.
HTH!