One way of getting into the City Centre of Athens from the Airport is by taking the metro; the metro system in Athens is very clean and modern, and easy to use around the city.
Once you arrive at the metro station, you will need to buy your ticket from the ticket office, at which point you will need to check with them which platform you need to be on, depending on where you are traveling.
The cheapest way of getting from Athens Airport to the City Centre is by bus; at just 6 Euros per person, this is an incredibly popular option for budget travelers.
To buy your tickets for the bus services, you will have to purchase them from the small blue ticket office; once you leave the Athens Airport Arrivals Hall from the doors in the middle, turn right, walk along the pavement, and you will find the office.
For the quickest and most direct option, though definitely not the cheapest, taking a taxi from the airport to the city center is the most efficient mode of transport, particularly if you are traveling as a group or a family.