Incorrect apostrophe usage is a classic grammarians' bugbear, guaranteed not only to make your writing look sloppy and unprofessional, but to summon hordes of demon pedants to descend upon you and tear you limb from limb.
On the other hand, look at the correct apostrophe usage in that first sentence—it's so right, so satisfying!
But why is it hanging out there at the end of the word, like the S is tipping its cap? Well, if you don't already know, you will by the end of this fascinating, insightful article.
Apostrophe of omission
Apostrophes, like any other punctuation mark, are used for the sake of clarity. The problem is, the apostrophe has multiple functions that tend to get confused.
The apostrophe of omission is the most common sort, to show where you've tucked away bits of a word to make it easier to say. It's used for contractions, like “it's” (“it is”), “can't” (“cannot”), and “m'lady”--usually where you squish a word or two together and some letters drop out of the middle.
This includes words where the original phrase has dropped out of usage, such as “o'clock” (“of the clock”) and “Hallowe'en” (“All Hallows' Evening”).
Sometimes we also use it to contract the suffix “-ed”, when the “-ed” looks awkward. For example, “KO'd” (“knocked out”), or ad hoc (totally made up) verbs like “cowabunga'd”.
There are also abbreviations such as “the '50s” instead of “the 1950s”, or “'til” instead of “until”, though in the case of the latter, the apostrophe has dropped out of common usage and we often use “till” instead.
Apostrophes can be possessive. Sometimes you have to tell them, “Apostrophe, this relationship is not going to work unless you give me some personal space.”
Possessive apostrophes indicate—as you might have guessed—ownership, and the apply to nouns. For example, “The dog's kennel”. “The bee's knees”. “Her Majesty's Secret Service”. “Future Content's dazzling portfolio”.
Essentially this involves tacking “-'s” to the end of the noun. There are a couple of exceptions to this rule, however.
If a singular noun already ends with an S, or an S-like (sibilant) sound, you have to keep the apostrophe but you can drop the second S. For example, “Chris' article”--so the apostrophe is hanging at the end. It wouldn't be wrong to write “Chris's article”, though.
If the noun is a plural, you have to drop the second S and put the apostrophe at the end of the word. For example, “The workers' rights”. “The sisters' cauldron”. “The grammarians' bugbear”.
Grievous common errors
Once you've got these rules covered, you're more or less good to go. But here are three extremely common errors to watch out for.
#1: Confusing “it's” and “its”. The possessive apostrophe does not apply to pronouns. You should only use an apostrophe if you're contracting “it is” (e.g. “It's the circle of life”), not if you're using the possessive “its” (as in “the lion ascended its throne”).
See also: “you’re” (“you are”) and “your”.
#2: The greengrocers' apostrophe. This is the nickname for when an apostrophe is added to a straightforward plural noun. E.g. “Buy your green apple's here” or “Employee's only”. An apostrophe should only be used in this way with possessive nouns.
There is a possible exception to this when you're using numbers, such as “the 1970's” or “1000's”, but this is usually redundant. It's more acceptable in American English than it is in British English.
#3: Misplacing the apostrophe in the plural possessive. I.e. putting the apostrophe before the S that denotes plurality. So if you were talking about multiple workers and wrote “the worker's rights”, that would be wrong. The apostrophe should be at the end.
Please note that in Grammarland, these are all capital offences.
Pass this on to your kids, and your kids' kids
Bearing in mind these simple rules, never again will you stumble into ineptitude, the laughing stock of all of literate society.
Actually, to be honest, you'll probably still typo it. You will. You will f*** it up. Remembering these rules will not save you.
Good luck, and my regards'.