Learn French: D'abord, vous devez réparer la table. - First, you must repair the table.

D'abord comes from de + abord (literally "at first"). When giving instructions or telling a story, it almost always goes at the very beginning of the sentence, usually followed by a comma, just like "First," in English.

I've learned the word premièrement. Can I use it instead of d'abord here?

You can, but d'abord is much more natural for everyday conversation and simple instructions. Premièrement (firstly) sounds a bit more formal, like you are reading from an official list or giving a speech.

Why is réparer not conjugated to match vous?

Because it immediately follows the conjugated verb devez (must / have to). The rule in French is that when two verbs are used together like this, only the first one gets conjugated. The second verb stays in its infinitive (dictionary) form.

How would this sentence change if I were speaking to a close friend?

You would use the informal "you" (tu) instead of vous, which means you also have to change the conjugation of the verb devoir. The sentence becomes: D'abord, tu dois réparer la table.