Agreeing in Number
The Rule: Pronouns and their antecedents must agree in number and gender.

What's a pronoun?
Pronoun Forms
                Subjective Objective Possessive Reflexive
Feminine She Her Hers Herself
Masculine He Him His Himself
Neuter It It Its Itself

What's an antecedent?
Antecedents are the words to which pronouns refer.

Examples:

  1. Matthew carefully selected his lobster from the tank.  (Matthew is the antecedent.)
  2. The gourmets selected their lobsters from the tanks.  (The word gourmets is the antecedent.)
Sexist example:
A humanistic teacher acknowledges that his students are people with human foibles.

Nonsexist but incorrect:
A humanistic teacher acknowledges that their students are people with human foibles.  (Singular antecedent, plural pronoun)

Nonsexist, correct but a little awkward:
A humanist teacher acknowledges that his or her students are people with human foibles.

Nonsexist, correct:
Humanistic teachers acknowledge that their students are people with human foibles.

Nonsexist, correct and the best revision:
Humanistic teachers acknowledge that students are people with human foibles. (Omit the pronoun entirely without substantial loss of meaning)

Indefinite Pronouns as Antecedents
 
Singular Indefinate Pronouns Plural Indefinate Pronouns
Anyone, Everybody, None, Others All, Both, Most, Some, Others

Examples:

  1. Anyone wishing to be considered for an award must submit his or her work to the panel of judges.
  2. All send their best regards.
Exercises Link

The examples I am using to illustrate pronoun and antecedent agreement come from the following source:
Frazer, Cynthia L. The Beacon Workbook.  Boston: Houghton Mifflin, 1990.