Learn French: Respirez profondément et levez-vous lentement.

Because this is a command (the affirmative imperative). Normally, reflexive pronouns go before the verb (like in vous vous levez). But when telling someone to do something, the pronoun moves after the verb and attaches with a hyphen.

If I want to tell a single friend to get up, how do I change levez-vous?

You would say lève-toi. For informal commands using the tu form, the ER verb drops its final 's' and the reflexive pronoun te changes to toi, attaching to the end of the verb with a hyphen.

Why isn't there a vous before respirez?

Because it is a direct instruction. Just like in English where we say "Breathe!" instead of "You breathe!", French drops the subject pronoun when using the imperative form to give commands or advice.

What does the -ment ending on profondément and lentement mean?

The -ment ending in French works just like the "-ly" ending in English to create adverbs. For example, lentement is built from the feminine adjective lente (slow), so it turns into "slowly."