Double-click on any word and see its definition from Cambridge Dictionaries Online.

Briefly, we can say that apostrophes have three uses:

1) To show possession in nouns

We add an apostrophe and "s" after all singular nouns and after plural nouns that do not end in "s":

Susan’s book; Pete’s dog; the children’s toys; the men’s room.

We add an apostrophe without "s" after plural nouns ending in "s":

The Beckhams’ mansion; the dogs’ dinners.

Note that we do not use apostrophes with the possessive pronouns hers, its, ours and yours, but we do use them with possessive pronouns that end in "-one" or "-body":

			Give the cat its dinner; Those books are ours.
			It must be somebody’s; Everyone’s papers are on the table.

2) To represent missing letters

We use apostrophes in contractions like:

Didn’t (Did not); There’s (There is); We’ll (We will)

(3) In some plural forms

Some sources (e.g. Practical English Usage, Michael Swan, Oxford University Press, 1997) indicate that we can use apostrophes if we want to make a plural form of a noun that does not normally have one:

I am afraid there are too many if’s and but’s for me to approve the plan.

The same source suggests that they can also be used in the plurals of letters, and with abbreviations and numbers:

			The manager crossed the t’s and dotted the i’s of the document.
			The 1990’s were very exciting years (also 1990s).

Other sources (e.g. Apostrophe Protection Society), however, indicate that apostrophes have no place in plurals because they do not represent missing letters or possession, and that the examples above should be written:

			I am afraid there are too many IFs and BUTs for me to approve the plan.
			The manager crossed the Ts and dotted the Is of the document.
			The 1990s were very exciting years.

The same source points out that this sort of use is more appropriate to spoken English than written English, and that in the latter the best option would be to write the sentences in a different way in order to avoid the use of apostrophes:

			I am afraid there are too many uncertainties for me to approve the plan.
			The manager corrected / approved the document.