How did Greek architecture influence modern architecture?
In two ways.
(1) Directly: In certain periods, such as the "Greek Revival" (1820s, I believe), Greek architecture was directly imitated.
(2) Indirectly - Greek architecture influenced Roman architecture, which influenced Renaissance architecture (apx 16th c.) and neo-Classical architecture (17-18th c.) in Europe, which had a world-wide influence. As in literature, philosophy, math, science, and so many areas, Greek civilization provides the basis of what comes afterward.