It is impossible to get around Rome without doing some walking, but you can always grab a taxi for short distances. From the Vatican, your best bet is to walk to the S. Pietro Train Station from where you can catch the regional train that runs between Rome and Civitavecchia. That train starts at Rome's main Termini Station and makes a stop at S. Pietro about 25 minutes later. From S. Pietro it is about 45 - 55 min to the Civitavecchia stop. At Civitavecchia, you exit the station and turn towards your left. It is than a very easy 4 block walk to the port entrance where you can get the free shuttle bus to the ship.