By metro
My apartment is very close to Holargos metro station (blue port-airport line). There are trains every 3-6 minutes. Trip duration is 15 minutes. Total time from my door to the center is 25-30 minutes. More information about first and last trains here. Tickets cost 1.20€ and are valid for 90 minutes. With this ticket you can go anyware except airport. More information about tickets here.
The central stations in blue line are Syntagma (Parliament) [7stops] and Monastiraki [8stops]. In red line Acropoli (just change line at Syntagma) [7+1stops].
Also Thission (green line), Keramikos (blue line) and Ononoia sq. (red line)
by bus/taxi
Metro is by far the easyest way to access city center. On rare occations when metro is not available you can use A5 and B5 buses, or taxi (if its late for example or there is metro strike). Taxi will cost around 15 euros (20 minutes).
Read more: My apartment is located in a strategic location to access Airport, Port, Bus and Railway stations