Gender is only an issue with singular pronouns. When the pronoun refers to a male, "he" or "him" should be used. If the pronoun refers to a female, then "she" or "her" should be used. If the noun being replaced is an object that has no gender at all, such as "book" or "fence," then "it" should be used. If the noun being replaced refers to something that has an unknown gender, then "he or she" may be used: "The mechanic will make a careful inspection before he or she makes a recommendation."
Plural pronouns are always neutral in gender. Due to their gender neutrality, the third person plural pronouns, "they," "them" and "their," are often incorrectly used in place of the longer "he or she," "him or her" and "his or hers." For example, when discussing licensing requirements for registered nurses, it is incorrect to say "A registered nurse must have their four-year degree." The rules of pronoun antecedents require either, "A registered nurse must have his or her four-year degree" or "Registered nurses must have their four-year degrees."
Determining a noun's status as a subject or an object requires examining its relationship with the verb. If the noun is responsible for the action described in the verb, then the subject pronoun should be used. If the noun is on the receiving end of the action, then the object pronouns are used. For example, if Sarah gave the book to Daniel, then, when Sarah tells the story, she will use a subject pronoun for herself and an object pronoun for Daniel, and say "I gave the book to him."
A common error in pronoun-antecedent agreement is to use "I" when "me" is the appropriate choice. This is usually due to confusion from a compound noun such as "Jessie and I" or "Jessie and me." To determine which is correct, simply the noun to just the first-person pronoun and see which is correct. For example, "Jessie and I went to the candy store," is correct, and so is "The owner gave Jessie and me a free chocolate bar."
By definition, the antecedent must come before the pronoun, not after. Furthermore, writers should remember that readers instinctively look for the closest noun to determine what the pronoun refers to, so a sentence like "Paul and Eric took turns feeding the pregnant cat, but she only allowed him to get close" creates confusion. If the beginning of the sentence is revised to "Paul took turns with Eric feeding the cat," then there is more distance between the pronoun and Paul, which makes it clearer that Eric is the antecedent.