An apostrophe is one of these: ’

It is NOT one of these: ‘
That is an inverted comma (or quotation mark/speech mark), which is used for opening quotations.  ’ is also used to close a quotation, in which case it is also an inverted comma.

It is also NOT one of these: `
That is a backtick, which is used for writing computer code.

Apostrophes are used in two cases: possessives and contractions.

They are NEVER used in plurals, apart from some rare exceptions.

Possessives

In possessives apostrophes are used together with an s. For example:

John’s glasses
the company’s premises
the Managing Director’s office
the employee’s working hours
3 years’ experience
one month’s notice
your money’s worth
Seller 1’s knowledge
Acme sp. z o.o.’s articles of association
the President of the Competition Authority’s announcement

Note that the apostrophe and s always comes at the end of the possessor. Do not write things like this:

Acme’s sp. z o.o. articles of association
the President’s of the Competition Authority announcement
Seller’s 1 knowledge

Remember to use this form instead of the structure with “of” – the company’s premises sounds more fluent that the premises of the company. For more on this see the posts in this blog entitled Careful how you use the word “of”.

When the possessor is a word or a name that ends in an s you should add ’s if the ’s is pronounced, e.g.:

the bus’s wheels
James’s book
Tom Jones’s singing

If the ’s is not pronounced you should only add the apostrophe, e.g.:

Socrates’ philosophy
Aristophanes’ plays

When the possessor is plural, you should only add an apostrophe without the s, as in
3 years’ experience above. More examples:

the delegates’ hotel
the companies’ premises
employees’ cars
shareholders’ meeting

Irregular plurals can be an exception to this rule (where the noun is plural but doesn’t end in s – use ’s). For example:

children’s clothes
men’s shirts
women’s hairdressers

Apostrophes are NOT used in possessive pronouns:

The company has not amended its articles of association to reflect the changes in the law. – NOT it’s

We have amended our articles of association. Have you changed yours? – NOT your’s

We have amended our articles of association. But they haven’t changed theirs. – NOT their’s

Writing it’s instead of its is one of the most common mistakes people make with apostrophes. Remember it’s is a contraction, and not a possessive.

Contractions

Contractions are shortened forms of words where some letters have been left out. The apostrophe goes where the omitted letters should be. Here are some examples:

it is / it has                 –          it’s
she will                        –          she’ll
we are                         –          we’re
I have                          –          I’ve
who is / who has      –          who’s
he had / he would    –          he’d
is not                           –          isn’t
have not                     –          haven’t
will not                       –          won’t
fish and chips           –          fish ’n’ chips
rock and roll             –          rock ’n’ roll

Not used in plurals

Never use apostrophes in plurals. This includes abbreviations:

He had over a thousand CDs. – NOT CD’s
Due to the new law we have to amend our T&Cs. – NOT T&C’s

But there are certain rare exceptions when you do use apostrophes in plurals:

How many r’s are there in “Mediterranean”?
How many 2’s are there in your phone number? (2s is also correct)

In British usage calendar decades are written like this: 

The company was established in the 1990s. 

But American usage requires an apostrophe: 

The company was established in the 1990’s.