Learn Hardcore French: Je dois rendre le livre demain.

rendre (quelque chose à quelqu’un/quelque part): to give back to the owner/issuer. Natural for library books: rendre le livre à la bibliothèque.
retourner: to go back (to a place) or to turn over; also “to send back” goods to a seller: retourner un colis au vendeur. Not used for giving a loaned book back to a library in everyday French.
rapporter: to bring something back to where you got it: rapporter un livre à la bibliothèque (possible, focuses on physically bringing it back).
ramener: to bring back (often a person, but can be an object). For a library book, rendre is the safest, most idiomatic choice.

Where does demain go in the sentence?

Most natural placements:

End: Je dois rendre le livre demain.
Fronted for emphasis: Demain, je dois rendre le livre. Avoid splitting the object and the verb with demain in neutral style (e.g., Je dois rendre demain le livre sounds stiff).

How do I say “I don’t have to return the book tomorrow” vs “I mustn’t return the book tomorrow”?

Don’t have to (no obligation):
- Je n’ai pas besoin de rendre le livre demain.
- Je ne suis pas obligé de rendre le livre demain.
- Je n’ai pas à rendre le livre demain.
Mustn’t (prohibition/advice not to):
- Je ne dois pas rendre le livre demain. (commonly understood as “mustn’t/shouldn’t”)
- Il ne faut pas que je rende le livre demain.

Could I use the future: Je devrai rendre le livre demain?

Yes, but it changes the nuance:

Je dois rendre le livre demain: current obligation concerning tomorrow (the everyday, natural choice).
Je devrai rendre le livre demain: the obligation will arise in the future, or you’re projecting about tomorrow’s duties (more detached/planned).

If I replace le livre with a pronoun, where does it go?

Before the infinitive:

Je dois le rendre demain. (not: ✗ Je le dois rendre) With a person recipient:
Je dois le lui rendre demain. = I must return it to him/her tomorrow.

How do I add who or where I’m returning it to?

Use à for the indirect object:

rendre le livre à la bibliothèque
rendre le livre à Marie With pronouns:
Je dois le lui rendre demain. (it + to him/her) If you include a place pronoun:
Je dois le rendre à la bibliothèque demain.
More compact but formal/rare in speech: Je dois l’y rendre demain. (it + there)

Why is it le livre and not un livre, mon livre, or ce livre?

le livre: the specific book known from context (most natural if both speakers know which book).
un livre: any book, not specific.
ce livre: this/that particular book (pointing it out).
mon livre: my book (ownership). For a library book, le or ce is usually better, though people sometimes say mon livre meaning “the book I have.”

How is devoir conjugated here?

Present tense:

je dois, tu dois, il/elle/on doit, nous devons, vous devez, ils/elles doivent Useful past forms:
j’ai dû (I had to), je devais (I had to/was supposed to, ongoing/background)

Can I say the same idea with falloir?

Yes:

Il faut que je rende le livre demain. Note the subjunctive rende after il faut que. Nuance: slightly more impersonal/neutral than je dois.

How do I pronounce the sentence naturally?

Tips:

je ≈ “zhuh” (often reduced: “j’”)
dois ≈ “dwah”
rendre ≈ “rahn-dr” (nasal vowel in -en-; final -e silent)
le ≈ “luh” (often very light)
livre ≈ “leevr” (French uvular r)
demain ≈ “duh-ma(n)” with nasal ending Liaison is common between dois and rendre: dois‿rendre sounds like “dwaz-rendre.”

How do I ask “Do I have to return the book tomorrow?” in French?

How can I say “by tomorrow” or “before tomorrow”?

avant demain: before tomorrow.
d’ici demain: by tomorrow (between now and tomorrow).
pour demain: for tomorrow/with tomorrow as the deadline (common for homework/tasks). Examples:
Je dois rendre le livre d’ici demain.
Le rapport est pour demain.

How do I talk about the past with these verbs?

How do I say “I should return the book tomorrow” or “I’m supposed to…”?

Do I need a preposition before the infinitive after devoir?

No. It’s devoir + infinitive with no preposition: