There are different buses that leave from the airport, just outside arrivals. Bus X95 (SYNTAGMA – ATHENS AIRPORT EXPRESS) will take you to Syntagma square (city centre – connection with metro lines 2 & 3). It departs every 15-20 minutes and it takes approximately 45 minutes to Syntagma square. There are several stops before Syntagma square as well. There are routes also at night.
You can check the routes of all buses leaving from airport here or by calling at 11185.
Tickets are available at the ticket kiosk at the bus departure area and at all metro stations around Athens. Finally, you can buy a ticket inside the bus by the driver.
Attention: You need to keep your ticket until exiting the station of your destination.