Judging from his expression, he's in a bad mood.

Literal

Expression [from-から] judging [conditional-と] he [topic-は] mood [subject-が] bad.

表情から判断すると — 判断する means 'to judge.' と marks the conditional. 機嫌が悪い means 'in a bad mood' — 機嫌 specifically refers to someone's mood or temper.