From the airport to Athens or the ports. See also http://athensairportbus.com/en/index_en.htm

 

On arrival at the airport of Elefthérios Venizélos of Athens, inaugurated on the occasion of the 2004 Olympic Games, you can either go directly to the port in order to leave for an island as soon as possible, or you can first go to Athens.

From the airport to the centre of Athens:

Since the year 2004 there is a direct metro connection with the centre of the city: line 3 runs from 6.3am to 11.30pm, each half hour –  you have to take the direction of Aigaleo, all the way to the stations of Sýntagma or Monastiráki.

When leaving the air terminal (for instance via exit 4) you take a left, until you get to the left of the Sofitel hotel. The footbridge takes you directly to the departure hall of the metro.

 

There is also the bus line 95 to the centre, final stop at the square of Sýntagma. You find this bus next to the exit, on the right of exit 4 (you should watch out to catch the right bus - 96 goes to the Piraeus!) – you should not forget to buy tickets at the kiosk beforehand.

From the centre to the airport:

You can take the metro line 3 to the airport in the stations of Monastiráki or Sýntagma – from the stations of Omónia or Akrópoli you first take line 2 to Sýntagma.
The metro line 3 goes in the direction of Ethnikí Amína and Doukíssis Plakentías; it is a good idea to wait for a metro continuing to the airport ("airport" is mentioned at the front of the first carriage) – otherwise you have to change in one of the two possible terminal stations. Every 30 minutes there is a metro with the airport as its final destination – you should buy the special ticket (2,5 €) at a kiosk beforehand.

From the airport to the Piraeus:

For the moment, de best solution is to take the metro: you have to take metro line 3, direction Aigaleo, all the way to the station of Monastiráki; here you have to change to line 1 to the Piraeus. From there it is a few hundred metres to the water side and then, by taking a left, to the large café with a beautiful terrace of the OLP (the port authorities of the Piraeus), where you can also leave you luggage – ticket offices are situated close by.

In earlier days, the only direct connection between the airport and the Piraeus was bus line 96. This bus still exists and also leaves on the right of exit 4. There is a bus every 20 minutes, but when there is a lot of traffic the ride can take up to one hour and a half. The final stop is on the Tselépi quay, nearby the same café.

The boats to the Eastern Cyclades (f.e. Amorgós) leave from gate E7 (nearby the café); the boats to Aigína, Póros, Hýdra and Spétses leave from gate E8 and the boats to the Western Cyclades (Sérifos, Sífnos, Mílos...) leave from gate E9.
The large Blue Star boats (Mýkonos, Santoríni, Páros, Náxos, Ios...) usually leave from gate E7 as well.
But in fact, you should inquire about the exact place of departure when bying your ticket. See the map of the port of Piraeus.

From the airport to Rafína:

For the boats to Andros (Gávrio) and also to Tínos and Mýkonos you have to go to the port of Rafína. Bus 2 going to Rafina leaves on the left-hand side when leaving the airport terminal, at the footbridge to the metro station, opposite hotel Sofitel. The ride takes half an hour, and from 6.10 am onwards there are buses practically every hour.

From the airport to Lávrio:

For the boats to Kéa you should go to the small harbour of Lávrio. Bus 15 to Markópoulo also leaves on the left, near the footbridge and opposite hotel Sofitel; in Markópoulo you should take bus 10 to Lávrio. Bus 15 only goes once every two hours; the first one at 6.40am and from 9.10am onwards every two hours (11.10am...).

Taxi’s are to be found on the left of exit 3.

From the centre of Athens to the Piraeus:

Metro line 1 connects the Piraeus and the centre and the north (Kifissiá) of the city. In the centre you can take the metro at the square of Omónia or in Monastiráki. At the terminal station of the Piraeus you go left and then via the footbridge over the busy street. All the way to the right you find the boats to Crete; the Blue Star boats (Mýkonos, Santoríni, Páros, Náxos, Ios,...) are usually to be found on the opposite side and to the left you can go to the Tselépi quay (gate E7 Eastern Cyclades): over here you see the large café, with shaded outdoor terrace, of the OLP (the port authorities of the Piraeus); over here it is very pleasant to wait for your boat. Ticket offices are nearby. 

The boats to the Eastern Cyclades (f.e. Amorgós) leave from gate E7 (nearby the café); the boats to Aigína, Póros, Hýdra and Spétses leave from gate E8 (more to the left) and the boats to the Western Cyclades (Sérifos, Sífnos, Mílos...) leave from gate E9 (even more to the left).
However, you should always inquire about the exact place of departure when bying your ticket.