Learn Spanish (Spain): Les regalamos un coche.

Les is an indirect object pronoun, meaning "to them" or "for them". We are giving the car to them, so they are receiving the action indirectly. If we used los (a direct object pronoun), it would mean we are literally giving the people themselves away as a gift!

Why use regalamos instead of damos if they both mean "we give"?

Dar is the standard verb for "to give", but regalar specifically means "to give as a gift". Since a car is usually given as a present in this context, regalamos is the perfect verb to use.

The translation says "We are giving", so why aren't we using the present continuous tense?

In Spanish, the simple present tense like regalamos is frequently used for actions happening right now. While you could say les estamos regalando, simply saying les regalamos is a very common and natural way to say "we are giving".

Where is the word for "we" in this sentence?

It is built directly into the verb! The -amos ending on regalamos tells us the subject is "we". You could add nosotros at the beginning, but Spanish speakers usually drop it unless they want to emphasize that we are the ones giving the car, not someone else.