First rule: If you change one word (noun, pronoun, verb) to maintain agreement within a sentence, you usually have to change at least one other thing – another pronoun, or the ending of a verb, and yet another pronoun, and so on.
Second rule: Keep agreement between pronouns—pronouns that refer to the same thing—within paragraphs, at least, and preferably throughout an entire piece of writing. This means considering also agreement between nouns/pronouns and verbs.
Third rule: Pronoun agreement has nothing to do with pronoun case. The two are entirely different issues. Agreement does not alter or even affect case and vice versa. So, while it’s necessary to consider both when writing with grammatical correctness, I strongly recommend that you never try to consider both simultaneously, or even in relation to each other.
PRONOUN AGREEMENT: NUMBER: singular or plural (we’ve talked about this )
PERSON: First person (I, we) — Second person (you) — Third person (he, she, they, noun)
GENDER: male, female, neuter (we’re not going to spend much time on this)
Of these, PERSON is the area of agreement that gives the most trouble. It may help to consider 3rd person by the definition of a noun, i.e., as a “person, place, or thing” – something objectively outside of myself (which would be 1st person) and outside of or away from someone to whom you are speaking directly (which would be 2nd person).
FIRST PERSON SECOND PERSON THIRD PERSON also 3rd person:
singular: I, me you he, she, it, him, her any NOUN
my, mine your, yours his, her, its, hers any indefinite pronoun (anyone,
nothing, someone, everybody, etc.)
plural: We, us you they, them demonstrative pronouns (that, this)
our, ours your, yours their relative pronouns (who, whom, which)
NOTE: “one” (as in “One should do xyz if a building is on fire”) is kind of in a class by itself in that if it is used once, the use should continue. The usage is rare nowadays. “One” is in 3rd person.