A pronoun must agree with its antecedent in number, person, and gender. Errors arise with collective nouns (the team … they/it?), indefinite pronoun antecedents (everyone … their/his?), and compound antecedents joined by or/nor. Modern usage increasingly accepts singular 'they' as the standard pronoun for indefinite and gender-neutral antecedents.
Focus on the trickiest categories: indefinite pronouns (anyone, each, everybody) and collective nouns. Revise sentences with errors, then justify each correction with the applicable rule.
You already understand subject-verb agreement — the rule that a verb must match its subject in number ("she runs," not "she run"). Pronoun-antecedent agreement is a parallel constraint, but it governs a different pairing: the pronoun must match its antecedent (the noun it refers back to) in number, person, and gender. When you write "The doctor finished her rounds," the pronoun "her" must agree with "the doctor." Change the antecedent to "the doctors" and the pronoun must change to "their." The principle is simple; the difficulty lies in the cases where the antecedent's number is genuinely ambiguous.
The trickiest cases involve indefinite pronouns — words like "everyone," "someone," "each," "nobody," "either," and "any." Despite their apparent plural feel (everyone means "all people"), these pronouns are grammatically singular in traditional formal grammar: "Everyone brought *his or her* lunch." The awkwardness of "his or her" in every sentence is one reason singular "they" has become the standard solution: "Everyone brought *their* lunch." Modern style guides including the Chicago Manual of Style, the APA, and the MLA now endorse this usage. Singular "they" has a long history in English — Shakespeare used it — and its acceptance reflects description of actual language use rather than a new invention.
Collective nouns create a different challenge. Words like "team," "committee," "class," and "jury" name a group but are grammatically singular in American English. "The team won *its* championship" uses a singular pronoun. However, in British English, collective nouns frequently take plural pronouns: "The team won *their* championship." Neither is wrong in its own dialect, but you should apply the convention consistently within a document. The confusion arises when writers shift between singular and plural mid-passage: "The committee submitted *its* report, and then *they* adjourned" — pick one and stay with it.
Compound antecedents follow a simple rule with a surprising exception. Antecedents joined by "and" take a plural pronoun: "Maria and James brought *their* laptops." But antecedents joined by "or" or "nor" follow the proximity rule — the pronoun agrees with the antecedent closest to it: "Neither the students nor the teacher had *her* notes" (teacher, singular, is closest). This feels counterintuitive at first, but the logic is that "or" and "nor" present alternatives rather than combinations, so only the nearest referent is grammatically active for agreement. When applying this rule produces an awkward sentence, rewrite rather than force the agreement.