Contractions are pretty easy, but as I often do, I started looking at something kind of interesting and fell down a rabbit-hole of exciting historical usage studies! I assume you are all withering with glee at the possibility of links to old books that weren’t interesting when they were published. Let’s start by looking at how contractions are punctuated.
It is generally stated without qualification by grammar books that in a contraction, the apostrophe goes where the letter(s) have been removed. That works great for a lot of contractions, such as shouldn’t, wouldn’t, needn’t, oughtn’t, mightn’t, hadn’t, aren’t, I’m, we’ll, you’d, they’ve, it’s, would’ve, should’ve. The rule also works in some non-contraction situations: o’clock, O’Dell, an’ (for and), havin’, etc. But it doesn’t work for some less standard contractions like hafta (not *hav’ta), shoulda (*should’a), wanna (*wann’a), gonna (*go’n'a). And it doesn’t work for two big contractions: won’t (not *wo’n't) and shan’t (not *sha’n't).
To be fair, the ignorance of hafta and the like in the grammar rules isn’t surprising since most all grammarians consider these contractions things that shouldn’t be written in English. (Not because they’re too new – I’ve managed to find gonna attested in 1899.) Of course, it does lead to the question of why it’s so clear to native English speakers that wanna doesn’t have an apostrophe. Apostrophes are productive; it’s not that you learn the contractions into which apostrophes go, and never use an apostrophe in other contractions (witness the great Pittsburghian restaurant Eat ‘n Park, with a productive apostrophe on the and contraction). Why no one writes wann’a is unclear to me, but I think most everyone would share the intuition that it would remove a terrific weight from your chest if only that apostrophe weren’t in wann’a. So let’s leave this an unsolved problem for the moment.
The interesting cases are wo’n't (from woll not, a variant of will not that had some currency back in the day) and sha’n't (from shall not, as said by me and other putting on airs). These look crazy, right? But why? At first I was thinking it’s some sort of constraint we all share that you oughtn’t have two apostrophes in a single word. That would explain why I eat at Eat ‘n Park (the place for smiles) and not Eat ‘n’ Park. But that’s not quite it; a quick Google search turns up ~500K hits for O’Donnell’s and ~75K for O’Dell’s, so it’s not impossible to have two apostrophes in a word. I’ve definitely seen examples of ‘n’ for and, and in fact the two apostrophes look more natural than one to me.
Did the contractions won’t and shan’t spring into English fully formed, like Athena from Zeus’s noggin? No, interestingly. Samuel Johnson’s Dictionary (printed in 1855), has wo’n't, as do some (modern) editions of Lewis Carroll’s Alice in Wonderland and The Ohio Educational Monthly in an article from 1868. Likewise, sha’n't was commonplace in the old days, plastered across the pages of the dreadful Victorian novels that I had to read in AP English as a lesson as to what happens to those who show an interest in reading. Books like Evelina; or, The history of a young lady’s entrance into the world (why did every single book in those days have to have a subtitle?)
Now the interesting thing is that won’t and shan’t live side-by-side with wo’n't and sha’n't in these old books. Some quick results on Google Books between 1600 and 1800: 777 won’ts, 57 wo’n'ts; 216 shan’ts, 73 sha’n'ts. Between 1600 and 1700: 48 won’ts, no wo’n'ts; 1 each of shan’t and sha’n't. So it seems it was never the case that the multiple-apostrophe form was more common. For some reason or another, English writers have always preferred a single apostrophe over strict application of “put apostrophes wherever a letter’s missing”. (Michael Quinion guesses that the double-apostrophe form was a later edition, suggested by logic-minded grammarians, that died out because it was a pain to write and looked weird.)
This single-apostrophe preference may be to blame for the rarity of double contractions like we’d've (which I use), couldn’t've (also good), or I’mn’t (which I definitely do not use). In fact, I might as well put in a plug here for double contractions, of which I’m a big fan, but it seems too few people are. Sprinkle some who’d'ves into your writing sometime. It’s superfun; your cheerfulness will increase at least twice as much from a quick double contraction as from an emoticon, I promise. ;) See? The emoticon just can’t compete.
The Preposterous Apostrophes series as it stands: