From the way he speaks, you can tell he's not American.
Literal
Way-of-speaking [from-から] he [topic-は] American not [nominalizer-こと] [subject-が] understand.
~ぶり is a suffix meaning 'manner, style' — 話しぶり ('manner of speaking'). Unlike ~方 which focuses on method ('how to do X'), ~ぶり captures the overall impression or character of someone's actions. から marks the evidence base for the deduction.