The crux of the biscuit ...

... is, of course, the apostrophe.

What's an apostrophe?  With that ph in the middle, it's got to be Greek, and so it is. As a rhetorical device, it means "turning away", as when Hamlet turns to address that skull (we're never sure just whose), and in general when a speaker switches from addressing those present to address someone or something not.

So how do we get from there to signs that say "Employee's only" and the eternal confusion between its and it's?  Let's start with the second item first.

For whatever reason, what stuck in my mind coming out of grade school was that the apostrophe was the way you formed possessives.  Finnegan's Wake.  Hobson's Choice.  David's blog.  That kind of thing.  And, by the way, it was also used for contractions.  Let's dance.  I'd've preferred not to.  But actually, I had it backwards.

In fact, the original use of the apostrophe is to indicate left-out letters.  If you squint just right, that makes the connection to "turning away".  Thus you'll see 'd all over the place in Elizabethan literature, a good clue that a past tense is going to be pronounced as we do now, without making a syllable of the -ed -- a consummation / Devoutly to be wish'd, as opposed to Of unimproved mettle hot and full, where the -ed gets its own syllable, as the meter dictates.  You'll also often see the -ed spelled out but not pronounced, so that's not a sure indication, but if it's not spelled out, you can be pretty sure it's not pronounced, either.

Written Elizabethan English uses this a lot more than we do, and not just for particular suffixes

• O, what a noble mind is here o'erthrown!
• My lord, you played once i' the university, you say?
• Use every man after his desert, and who should 'scape whipping?

The 's for possessives is just one more example of this.  Chaucer, living a couple of centuries before Shakespeare, would write -es, to be pronounced as a syllable:

• And in a glas he hadde pigges bones (again, the meter dictates that both the e in hadde and the es in pigges are pronounced)

We would write And in a glass he had pig's bones (never mind why).

The apostrophe seems to have more to do with pronunciation than omitting letters per se.  Where Chaucer wrote

• And specially from every shires ende

we would write, and Shakespeare would have written

• And specially from every shire's end

The e is still there, but silent, to make the i in shire long, and the two-syllable shires has become the one-syllable shire's.

Thus the apostrophe in the possessive is no different from any other apostrophe, at least etymologically.  The mystery, actually, is why we don't use it in plurals (except when we do -- more on that in a bit).  Chaucer's English uses -es for the plural as well as the possessive, giving it a full syllable

• Whan that Aprille with his shoures soote

By Shakespeare's time, it's both spelled and pronounced without the e, and with no apostrophe

• When April with its sweet showers

Why, exactly?  I don't know, and I can't be bothered to look it up.

Which brings us back to its.  The possessive pronouns my, our, your, his, her and their have been around in various forms as their own words forever (or at least, before people started using apostrophes in writing).  In Chaucer's writing, though, the possessive of it is his, as in the quote above.  The usage its only comes along later, by analogy with the other possessive pronouns.  As there was never any extra syllable to leave out, we have its from the start, and not ittes becoming itt's or it's.

If you buy that, it's not hard to see how we got to the present-day standard of apostrophe use

• Contractions, such as he'd and would've, but only a limited list.  The Apostrophe is no longer productive (meaning usable in new ways -- except when it is …)
• Possessives, like a dog's breakfast or Joe's garage.
• But not the possessive pronouns my, our, your, his, her, its and their

But how did we get from that to today's non-standard apostrophe use, particularly in forming the plural, as with the Employee's only sign (which I have actually seen)?  I really don't know, but my guess is that it started out in constructions where it's a bit odd to write a normal ending, as with 86'd.  You could well write 86ed, and people have, but presently it's much less common.  Probably spelling it out, 86ed, makes it harder to read, both because of the numbers and letters jumbled together, and perhaps because there's a little hesitation over whether to pronounce the e.

That makes the apostrophe a convenient way to break up number-letter combinations, and we get the 60's instead of (or as well as) the 60s.  Run into that enough, and it's easy to write employee's for employees.   Interesting, but is there any evidence?  Maybe …

Googling the sixty's gets you results for the sixties, with a link if you really want the sixty's, and sure enough there are more hits for the sixties.  But not a huge amount more.  Generally when there are two forms for a term, one gets many more hits than the other.  100:1 is not uncommon.  In this case, it's not quite that -- 29 million to 4 million.  Google hits are a fairly crude measure of how prevalent a term is, but good enough for our purposes here.  We're helped a bit here in that the sixty is not something you'd expect to possess anything, so most of those hits for the sixty's probably really are plurals.

On the other hand, "two babies" (I used "two" so that the baby's form is unlikely to be a possessive) gets around a million, while "two baby's" gets around 16,000.  I wouldn't read too much into two data points, but this at least suggests that constructions like the 60's are prototypical and constructions like two baby's are built from them by analogy, but not as readily.

I'm not condoning any of these usages, though I've been known to use constructions like 86'd and the 60's (and for that matter it's for its, but not so much after reading Eats, shoots and leaves).  You wouldn't want to advertise your skill's on your resume, but employee's on a handwritten sign somewhere is not a big deal.  My point, rather, is that non-standard usage is not a completely haphazard affair, any more than anything else to do with usage.  There is generally a reason, even if it's not likely to convince an English teacher or proofreader.

And don't even get me started on quotation marks.