Since March 2000 functions in Athens the new international airport Eleftherios Venizelos. All the domestic and international flights from and to Athens are landed there. In order someone to reach the new airport from the port and vice versa has to follow has the following options:
Bus Line X96 (Piraeus - International Airport Express) Bus line X 96 begins from the centre of Piraeus (Karaiskaki square) and reaches the airport via the avenues Posidonos, Varis-Varkizas and Varis-Koropi. The schedule lasts about 75 minutes but in peak hours perhaps lasts more. The ticket of the schedule costs 3 Euro and is valid for every other public mean of transportation for one day.
Metro (Airport - Monastiraki - Piraeus) Metro line 3 starts from Athens International Airport and finishes at Monastiraki station. Change there to metro line 1 (Piraeus - Kifisia) with direction to Piraeus. It takes 60 minutes to get from Airport to Piraeus and ticket price is 6,00 Euro. More info you can find at Athens Metro.