A direct object is a noun or pronoun that receives the action of a verb (answering 'whom?' or 'what?'), while an indirect object is a noun or pronoun that tells to whom or for whom the action is done. Not all verbs take objects, and understanding which verbs do helps you write grammatically correct sentences.
Identify action verbs in sentences, then ask 'what?' or 'whom?' to find the direct object, and 'to/for what?' or 'to/for whom?' to find the indirect object.
You already know that verb phrases are built around action verbs, and that action verbs describe something being done. Many verbs don't act in isolation — they transfer their action onto something or someone. The noun that receives the action directly is the direct object. To find it, take the verb and ask "what?" or "whom?" right after it: "She kicked the ball." Kicked what? The ball. That's the direct object. It completes the verb's meaning.
Some verbs can also involve a second noun — not what received the action, but who benefited from it or who it was aimed toward. This is the indirect object, and you find it by asking "to whom?" or "for whom?" about the action. "She gave him the book." She gave what? The book (direct object). She gave it to whom? Him (indirect object). The indirect object is always paired with a direct object — you can't give a recipient without also giving something, and you can't have an indirect object without a direct one to accompany it.
Word order matters, and English gives you two patterns. You can place the indirect object first and the direct object second, without a preposition: "She gave him the book." Or you can reverse the order and add a preposition: "She gave the book to him." These two sentences mean the same thing. The preposition ("to" or "for") signals the indirect object role when it doesn't come first. Notice that only the preposition-free order is grammatically allowed when the indirect object comes first — you can't say "She gave to him the book" without a specific reason to emphasize.
Not all verbs can take indirect objects. Ditransitive verbs like give, send, tell, show, buy, make, and teach allow both objects; monotransitive verbs like kick, see, and find take only direct objects. When you're unsure whether a sentence needs an indirect object, ask whether the verb involves transferring something to someone. If yes, you probably have a ditransitive structure and should look for both participants.