The apostrophe is used to show (1) possessives of nouns and some pronouns, (2) contractions, and (3) some plurals.
Possessives of Singular Nouns
Use an "apostrophe ‑s" to form the possessive of a singular noun, even if that singular noun ends in an ‑s. The rule also applies to people's names. Doubters should read Strunk & White's rule 1, on page 1. Study these examples, and remember that we're talking about the possessives of singular nouns:
This rule comes straight from the horse's mouth.
He followed the boss's policy.
The law displayed Congress's policy.
He enjoyed Dylan Thomas's poetry.
The media gathered at Paula Jones's press conference.
Bridget Jones's Diary (The movie got it right.)
Possessives of Plural Nouns
Use an apostrophe and no "‑s" to form the possessive of a plural noun. (Some irregular plurals not ending in ‑s require the use of an "apostrophe ‑s.")
The children watched the puppies' tails. The children's fathers watched, too.
Two Nouns Jointly Possessing
When two or more nouns possess the same thing, add "apostrophe ‑s" after the last one listed. When each separately possesses, add "apostrophe ‑s" to each one listed:
My aunt and uncle's house always intrigued me.
Sam and Kay's children played. (Sam and Kay are mom and dad.)
Sam's and Kay's children played. (Sam and Kay each have their own children.)
Possessives of Some Pronouns
Some indefinite pronouns have possessive forms shown by the "apostrophe ‑s":
The reciprocal pronouns also appear in possessive form. Note that these are always singular possessives, not plural possessives: