Learn French: Nous nous dépêchons, nous nous habillons maintenant ! - We are in a hurry, we are getting dressed now!

The first nous means "we" (the subject). The second nous is a reflexive pronoun, which in this case means "ourselves". Because se dépêcher (to hurry) and s'habiller (to get dressed) are reflexive verbs, you must include that second pronoun. Literally, you are saying "We hurry ourselves, we dress ourselves."

The dictionary says "to get dressed" is s'habiller. Where did the s' go in nous nous habillons?

The reflexive pronoun always changes to match the subject! The s' (a shortened form of se) is used for the infinitive dictionary form, as well as for the "he/she/they" forms. Since the subject here is nous (we), the reflexive pronoun must also change to nous (ourselves) to match it.

Do I pronounce the 's' at the end of the second nous in nous nous habillons?

Yes! Because the letter 'h' in habillons is silent, the word essentially starts with a vowel sound. This causes a "liaison" (a linked sound) between the two words. You will pronounce the 's' on the second nous like a "z", making it sound like "noo noo zah-bee-yoh(n)".

The English translation uses "-ing" ("getting dressed"). Is there a special "-ing" verb form here?