In English, the plural is formed with a final "s" or "es" most of the time. It is formed with an apostrophe 'S' only in a very exceptional circumstance. Thus one Fool, two Fools, one motley hat, two motley hats, and so on. NOT two Fool's, and not two hat's. NEVER. Well, except that you see this spelling catastrophe everywhere, but that doesn't make it right.
In many constructions, an apostrophe signifies possession. Thus, the "motley Fool's hat" is the hat of a single motley Fool (married or not). Or the "Fool's motley hat." Where we get thrown for a loop, of course, is with "its" and "it's," where "its" signifies possession and "it's" is the contraction of "it is." Yes, it's tricky. I've been known to screw it up myself and ignite a firestorm of posts on the Fribble message board. But if we can send a man to the moon, can't we get this right, America?
OK, now for the advanced course. First, there is possession by plural owners. This is spelled with a terminal apostrophe. Thus, the "motley Fools' hats" refers to hats owned by several Fools, and one could also imagine "the motley Fools' hat," a single hat owned by several Fools. The rule is very simple: several owners means you put the apostrophe after the word.
And the exception. This is perhaps what caused our national slide into spelling perdition. For some reason, not necessarily logical, it has become proper to use an apostrophe when spelling the plural of an acronym. Thus, one can refer to the "IBM's and TWA's" of the world, meaning that you are referring to several corporations of this type. You would refer to "IBM's" stock price or "TWA's" accident record with the same spelling, though you now are using the concept of ownership. But hey, you could lead a long, satisfying, fulfilling life, and NEVER use this exception.
So in the interest of the other 99.99% of uses, simply use the apostrophe ONLY when intending possession, and if you want to show off, use it before the 'S' when there is one owner, and after the 'S' when there are several owners.
I now hand the ball off to someone to carry on about the next-most-common ignoramus identifier, the misuse of "there is" and "there are." What is it about the phrase "There is two ways to speak English, Billie-Joe-Bob..." that raises the grammarian barbarian's eyebrow?