If you are thoughtful about how to reach Trevi Fountain, then it is in the middle of the city, and therefore, it is easily accessible on foot. The streets to the Trevi Fountain are so narrow the buses cannot access them; hence, the best way to get to the fountain from where the bus drops you is to walk.
The buses that transport people are popularly known as hop-on hop-off sightseeing buses and they stop near the fountain. Barberini is the nearest Metro stop and is 10 minutes’ walk from Spanish Steps. Another route to connect to the fountain is The Via Del Tritone, which is about 100 steps from Barberini. Bus 175 or 85 takes you up to Tritone.
Attractions near the fountain are the Spanish Steps also known as Pantheon. You get to visit the Spanish Steps and Piazza Navona from the Trevi Fountain. You can also choose to visit Colosseum and Roman Forum all while the guide keeps you enlightened about them all.
There is a Metro christened Spagna or Rome Metro that will take you to the Spanish steps. It is an underground station on line A of the Rome Metro.
Overall, walking through the city is the best way to capture most of the beauty. You can walk alone or take professional walks. Professional walks entail having a guide walk you for close to 3 hours where they enlighten you about Rome and make a great company.
The taxi or cab
If you choose not to walk or use the bus, you can use taxis or cabs that are easily available from Largo Chigi behind the Galleria Alberto Sordi shopping Mall. You can as well use the train, the Leonardo Express that leaves every 30 minutes.
To wrap it up, walking is the most reasonable way to get to all the tourist attractions from Trevi Fountain.