Picture a guy parked at "la mesa de siempre" (the usual table), glass in hand, telling himself he is drinking to forget. He says it straight in the first lines: "Tomando pa olvidarte" (drinking to forget you), and in the next breath admits "No dejo de quererte" (I can't stop loving you). When his friends are around he just goes along with them, but only "por el despiste", meaning as a cover so nobody notices he is still hurting.
The chorus is where it gets honest and a little funny in a sad way. "La depre me pegó bien y bonito" (the depression hit me good and proper) uses la depre, Mexican slang short for depresión, plus the set phrase bien y bonito, which literally means "well and pretty" but here means "hard". He also drops "La neta, estoy muy mal" (honestly, I'm in really bad shape), where la neta is Mexican slang for "the truth" or "for real". And "bien jodido" is a crude way to say he was left completely wrecked. No matter how drunk he gets, it changes nothing, and he ends up counting empty bottles: "A ver cuántas botellas más vacío" (let's see how many more bottles I empty).