Learn French: La mère demande à la garderie de surveiller le bébé. - The mother asks the daycare to watch the baby.

This is how you form an indirect command in French! When reporting that someone is asked to do something, you use a reporting verb like demander (to ask) or dire (to tell), followed by de and the infinitive form of the action verb. Here, it's demande ... de surveiller (asks ... to watch).

Why is it demande à la garderie and not just demande la garderie?

In French, you ask to someone. The full structure of the verb is demander à quelqu'un de faire quelque chose (to ask someone to do something). Because the daycare (la garderie) is the entity being asked, it acts as an indirect object and needs the preposition à in front of it.

How would I replace à la garderie with a pronoun to say "The mother asks it to watch the baby"?

Because la garderie is introduced by à, it is an indirect object. Since it is singular, you would replace it with the indirect object pronoun lui. The pronoun goes right before the main verb: La mère lui demande de surveiller le bébé.

Could I use regarder instead of surveiller for "to watch" the baby?