The subject of your sentence is that person, place or thing that is doing the action. In "the boy ran," the noun "boy" would be the subject of the sentence. If you replace boy with the pronoun "he" then the sentence would read, "he ran." Other subject pronouns include she, we, they, I and it. Subject pronouns can also rename the subject, and follow "to be" verbs such as is, are, was, were, am, and will be. "It was he who called," is the same as, "He called."
Object pronouns are those pronouns in which the action is being done to them. In the sentence, "Susan called Frank," Frank would be the noun who received the action. The pronoun that would take the place of this noun as the object, "Susan called him." Object pronouns include him, her, me, and them. These are the pronouns that are used whether the object is indirect or direct, or the object of a preposition.
Possessive pronouns include mine, yours, his, hers, its, ours, theirs, and whose. They can either modify the subject, "His leg was broken," or be the object, "The dog was hers." Unlike a possessive noun that requires an apostrophe, these pronouns do not require one. The only time "it's" requires an apostrophe is when it is combining the words "it is." Reflexive pronouns like myself, himself, herself, itself, themselves, ourselves, yourself, and yourselves refer back to another word in the sentence, and generally work as an object referring back to the subject. "I could eat that whole pie myself."
Clauses in a sentence contain a subject and a verb, such as "I walked home." Strong clauses can stand alone, whereas weak clauses require another clause in the sentence to complete the thought. "I walked home although I was tired." In this case, a strong clause, "I walked home," was rounded out by a weak clause, "although I was tired." Which pronoun you use depends on the clause structure, which you may have to isolate in order to determine. In the sentence, "He gave the book to her and me," you could break down the sentences as, "He gave the book to her," and "He gave the book to me."