I have spent about a year living in Athens. The original Athens Metro Line 1 (25.6km) from the port of Piraeus, through Athens centre and on north-eastwards to Kifissia, is the Green Line.
Piraeus is the port of Athens. You can take the Green Metro or Subway line from the port of Piraeus to downtown Athens. Tickets are 0.70 €.
You can take a taxi from the ship to the Piraeus Metro station and save a 20 minute walk. Cost will be a little over 5€
A note about taxis The meter *must* be running when they start off (there is an immediate charge of 1.00 euro) and it should show a (tariff) "1", . This is compulsory and you should insist. If the meter is not running you can say "Monno may metreeti" - meaning, only with the meter. It is quite normal for taxis to pick up other passengers en route, but everyone still pays the full fare for their trip (this is an accepted, though illegal, practice). Minimum fare is 2.70 euros.
Athens is a HUGE city. I will assume you want to go to the Acropolis. Simply get off at the Monistraki stop or the 7th stop. You will see the Acropolis from train. You can spend all day in the Monistraki area. The Monistraki Train / Metro station is
1 block or 1/10 mile from the entrance from the Acropolis heading South.
½ mile East is Syntagma - the Greek Parliament building and the tomb of the unknown soldier guarded by Greek soldiers wearing skirts. Women wait for hours hoping for a breeze.
30 yards West is the Placa, a touristy shopping district, but cool to walk through.
3/10 of a mile due North on Athenas Street is the Central Market with a lot of great little working class restaurants, authentic Greek food….reasonable non tourist prices.
6/10 of a mile due North of the Central Market is the National Archeological Museum which opens at 1:00 pm on Saturday.
3/10 of a mile North West of the Archeological Museum is Victoria Square….where you catch the train back to the port Pireaus
Google Athens Greece Metro to get a map of the Metro. You can't get lost. There is only one train in Piraeus. Simply get on the train that everyone else is on. It will leave the station. Trains run frequently, are safe and efficient.