After returning our rental car we need to travel to the cruise ship dock. How best is that done?
You can take the Leonardo Express from the airport to Rome Termini RR station, and then a train from there to Civitavecchia. Both trains are frequent. From Civit. you will want to take a taxi to the dock because it is a longish walk and you will have luggage. But you ask for BEST. Best would be to have a private transfer. Google "transfer from airport to Civitavecchia" for that info. Bound to be expensive. The best usually is.
If you can handle your luggage, the least expensive way to the cruise terminal is to take the FM1 from FCO to Roma Trastevere ( 5.50E about 35 mins ) then change platforms to catch the regional train to Civitavecchia ( 4.10E a little over 1 hr )We did this last year, and it was really simple. After getting off at Civitavecchia, it's no more than a 10 min walk to the port entrance, where there are free shuttle buses to bring you right to your cruise ship. Of course if you have too much luggage, then you'll just have to hire a car/taxi from FCO to Civitavecchia.
Both prior responses are accurate and provide for different options. Going into Termini COULD be faster depending on your timing and trains available. There are fast trains to Civit.. that take about 45 minutes. You should probably plan on walking from the Civit.. train station to the port entrance. There is a 1.10E mini bus to the entrance but line is long so you could waiting some time to board the bus. Taxis will be fairly expensive since it is less than half mile to the entrance, The walk is easy -- flat and along the beach. We have always walked it (four times) but our luggage is only three carryon size bags for the two of us so it is easy for us.