There’s a very easy rule for using apostrophes to indicate possession.
Here it is:
Now, that rule may not work in every case, but it’s pretty good. It handles some confusing cases fairly well, such as irregular plurals. Here are some examples:
bone belonging to one dog → dog‘s bone
bone shared by many dogs → dogs‘s bone → dogs’ bone
toy belonging to one child → child‘s toy
toy shared by many children → children‘s toy
car belonging to John → John‘s car
car belonging to Mr. Lewis → Mr. Lewis‘s car (or → Mr. Lewis‘ car, perhaps, according to taste)
When the bone belongs to a single dog, the ‘s is applied to dog, whereas when there are numerous dogs, it is applied to the plural dogs. In the latter case, dogs’s looks clumsy and is not correct, so the final s must be dropped to form dogs’. In the case of the irregular plural children of child, when you just add ‘s, nothing more needs to be done. In the case of names ending in s, it seems to be a matter of personal taste whether you leave the -s’s, or simplify it to –s’.
Remember that to form a (regular) plural, you just add s. The formation of neither regular plurals (such as dogs, formulas) nor irregular plurals (such as children, formulae, fungi) requires an apostrophe. Apostrophes are required when indicating possession, or abbreviation where an apostrophe indicates where letters are missing (such as don’t = do+not).
Probably the main remaining area of confusion is the case of the so called possessive pronouns. The weak forms are: my, your, his, her, its, our, and their. The strong forms are: mine, yours, his, hers, its, ours and theirs. The main source of confusion here is with its, probably because of the existence of the abbreviation it’s (= it+is).
In this case you just need to remember that its (belonging to it) is already a word in its own right. It no more needs an apostrophe than do his (not hi’s), hers (not her’s), yours (not your’s), ours (not our’s) or theirs (not their’s).