Pronouns are words that are used in the place of nouns. Usually a pronoun has a definite, easily recognized antecedent (the noun or pronoun to which it refers) with which it agrees in person, and number.

            The boy took his jacket off and left it in the hall. (third person singular noun, third
                        person singular pronoun)
            The guests left their coats in the master bedroom. (third person plural noun, third
                        person plural pronoun)

Each, every, either, neither, anyone, anybody, everyone, everybody, someone, somebody, no one, and nobody are singular, and pronouns referring to them should be singular.

            Everyone should take his or her (not their) turn.
            Neither of the students remembers his or her assignment.

Collective Nouns as Antecedents

A collective noun names a group of people or things: family, group, audience, class, number, committee, team, and the like.

When the group acts as one unit, use a singular pronoun to refer to it.

            The audience is cheering as it stands to applaud the performers.
               [The audience is acting as one unit, so the pronoun is singular.]
            The family is spending its vacation in Maine.
               [All the family members went to one place together.]

When the members of the group act individually, thus creating more than one action, use a plural pronoun.

            The audience put on their coats and walked out of the building.
               [Here the audience is acting as individuals, so the pronoun is plural.]
           The team will try on their new uniforms after school.
               [Each team member is trying on an individual uniform.]

Antecedents Connected by "Or" or "Nor"

When antecedents are joined by "or" or "nor," the pronoun agrees with the closer antecedent.
           Either the loudspeakers or the microphone needs its electric cord repaired. (singular
                    antecedent closer, singular pronoun)
           Either the loudspeaker or the microphones need their electric cords repaired. (plural
                    antecedent closer, plural pronoun)
           After the restaurant closes, neither the resident mice nor the owners' cats can manage to
                    get themselves a good meal. (plural antecedents, plural pronoun).