KTEL buses to Lavrio (€5.30, two hours, every 30 minutes) run from the Mavromateon terminal in Athens. Airport buses leave from the front of the arrivals hall near the Sofitel; you must change buses at Markopoulo. Both stop on the Lavrio quay.
Lavrio Port Authority and www.openseas.gr have ferry information.
Taxi Posidon can run you to the airport (day/night €40/55, 30 minutes) and central Athens (€60/80, one hour); fares are higher for pick-up in Athens or the airport. Lavrio to Cape Sounion is €12.