Newbie train question

Can a veteran traveler to Rome tell me how to get from the cruise port to our hotel in Rome that is right near the Trevi fountain by train?A private transfer costs 75 euros, but would like to attempt the train if it is not too much of a hassle.

Thanks in advance!

Sure, but you should know that €75 is a phenomenally good price, almost too good to be true, unless that's a per-person price in a shared shuttle.

From the cruise port to the train the usual route is the free port shuttle to the Via Turco/Largo della Pace exit, followed by the local Argo bus to the train station. The bus costs €2 and tickets can be purchased at the service center near the shuttle bus drop off.

If your ship is berthed in one of the close in southern spots (10, 11, or 12 on this map: http://civitavecchia.portmobility.it/sites/default/files/file_uploads/map_of_port_of_civitavecchia_eng_1465288193.jpg) you can probably walk to the train station faster than the shuttle bus plus local bus route but you need to be able to handle your luggage. The port shuttle bus will not stop near the southern (Fort Michelangelo) exit so that's not an option. Just a note about the map linked above, the top of the map is east, unlike a typical map so it's easy to get confused (or at least it confuses me).

If you decide to walk, the distance from the southern (Fort Michelangelo) exit to the station is fourth-tenths of a mile, from the central (Via Turco/Largo della Pace) exit it's one mile.

Trevi fountain is one of the few areas in Rome where it makes sense to take the train all the way to Termini station (most other locations can be reached faster by getting off at other Rome stations).

The nice thing about going to Termini is that it opens up more train options, since the high speed/non-stop trains only go there (for the most part).

The bad news about going to Termini is that if you use the regional train the tracks they use are a full three blocks from the station, so you've got a bit of a walk (four-tenths of a mile) from there to the buses or metro.

Therefore, this is one time I would recommend aiming for a more expensive train, to avoid the schlep at the Rome end and also because you are guaranteed a seat (the regional train is first come, first served and it's a heavily used commuter line, so seats into the city in the morning are a scarce commodity).

From Termini to the Trevi fountain you can take the metro, line A direction Battistini for two stops to Barberini (metro map here: http://atac.roma.it/files/doc.asp?r=4) or you can take a bus #71 (map here: http://viaggiacon.atac.roma.it/?service=trovalinea&linea=71&percorso=71AT).

Note: if you take a regional train, the #71 bus is closer to the auxiliary track heads than the metro. The bus stop is on Via Rattazzi, just a block from where you'd get off the train.