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- If one is occasionally drunk, you can say: "Está bêbado" (m), "Está bêbada" (f).
- If one's getting drunk is a habit, in other words, one is an alcoholic, you might want to say: "É (um) bêbado" (m), or "É (uma) bêbada" (f).
In my state we also say "bebum" and "borracho", but I believe those are not standard. Plus, if you want to sound technical or formal you should use "alcoólatra" when someone is addicted to drinking alcohol.