Learn Dutch: We geven de baby de speen, nu ze moe is. - We are giving the baby the pacifier, now that she is tired.

In Dutch, nu can be used as a subordinating conjunction, which links a main clause to a dependent clause. When used this way, it translates to "now that" or "since". You can tell it is acting as a conjunction here because it introduces a new clause with the verb pushed to the end (nu ze moe is).

Why is the verb is at the very end of the sentence?

Because nu (now that) acts as a subordinating conjunction here, it forces the clause it introduces into a "verb-final" word order. So instead of the standard Subject-Verb order (ze is moe), the verb gets pushed to the end: nu ze moe is.

Why isn't there a word for "to" before de baby, like aan de baby?

Just like in English ("We give the baby the pacifier"), Dutch lets you drop the preposition aan (to) if you put the recipient (the indirect object, de baby) right before the thing being given (the direct object, de speen). If you wanted to use aan, it would go after the direct object: We geven de speen aan de baby.

Could I use zij instead of ze in this sentence?