From central Athens, the easiest route is Metro Line 1 (the green line) — terminus stations Monastiraki (centre) to Piraeus, about 20 minutes, every few minutes. The metro station sits right on the waterfront, a short walk from the main ferry quays.
From Athens international airport, take Metro Line 3 westbound to Monastiraki, then change to Line 1 — total trip about an hour and ten minutes. The X96 express bus runs directly from the airport to the Piraeus ferry terminals, useful if you arrive late.
Long-distance ferries leave Piraeus for almost every Greek island. Tickets are best bought online (book in advance for August and major holidays) or at the agency offices on Akti Miaouli.