Gwen Mak
Together, we can stop apostrophe abuse!

I don't know when, I don't know how... but some time ago, someone started abusing apostrophes. I'm sure it started out innocently enough with a little confusion over possession. But unfortunately, this apostrophe abuse has gotten so out of hand that even my iPhone encourages it! Let's put an end to this abuse once and for all.
There are a total of TWO occasions upon which it is appropriate to decorate a word with an apostrophe:
To indicate possession
To indicate the omission of one or more letters
That's it.
To go into a little more detail, we'll start with the possessive apostrophe. This guy indicated ownership or belonging of one thing to another. There are singular and plural forms. Generally when the subject is singular, the apostrophe is placed before the s, and if the subject is plural, the apostrophe is placed after the s.
Possessive Singulars
Singular subjects use the apostrophe before the s, even if the thing being possessed or owned (the object) is plural:
Sienna's rabbit
that house's roof
this mall's escalators
library's books
Here, I need to mention a note on style. There is a classic little book by Strunk and White, called The Elements of Style. Many writers turn to it for advice and it has sort of set the bar for elevated writing. The very first rule in this book, first published in 1918, concerns possessive apostrophes:

Many grammar textbooks and guidelines will tell you that singular words ending with s should be made possessive by adding an apostrophe after the s; Charles' friend or Burns' poems. Both forms are correct, it's just a matter of style which you prefer in your own writing. If you go with Strunk and White, other people who know about The Elements of Style might notice and regard you as more cultured and civilised, whilst those who are unfamiliar either won't notice or will think you're wrong. In either case, at least YOU will know you've done it right and can pat yourself on the back for it.
Possessive Plurals
When a plural word ends with an s, make the possessive by adding an apostrophe after the s:
the shoes' finish
the Smiths' house
the boys' room
If the plural form of the word does not end with an s, make the possessive by adding apostrophe s:
women's decision
children's house

Contractions
Contractions are two words squished together to make a single word. To let people know that this word is a stand in for two longer words, we use an apostrophe in place of the letter or letters we've left out:
Can not | Can't
They are | They're
We would | We'd
You'll notice that you can see the origin of the contraction in the two word combinations that precede them in my examples. Word that don't have clear origins are not real contractions, like ain't... There's no word ai. Don't use words that are not real in your writing. If you're writing and aren't sure if a contraction is correct, replace it with the long hand, two word phrase and see if your sentence still makes sense. If it doesn't, you're using the wrong word.
Notable exceptions
It's and its are a common source of confusion. It's (with an apostrophe) is a contraction. The apostrophe is used to indicate the omission of the second i from it is. It's should only be used when it can logically be replaced by the non-contracted form, it is.
It's hot outside | It is hot outside
It's his birthday | It is his birthday
Its is the possessive form of it, meaning something belongs to it. Its should be used to indicate possession:
The bird flaps its wings : The wings belongs to the bird
The house is too big for its lot | The lot is associated with the house