Rome is an open-air museum and most of its attractions can be easily reached on foot or by public transport. 

My advice, the best way to visit Rome is by walking.

Here some info about the public transportation.

THE LINE BUS 64

The bus line 64, also known as the tourists line bus, is very useful for visiting the historical city center and the Colosseum area. The bus 64 starts from the San Pietro Train Station, it crosses all the entire city center from West to East by “Corso Vittorio Emanuele II”. The last stop of the 64 bus is Termini. To go to the Colosseum, get off at Venice Square, then walk 5 minutes “via the Via dei Fori Imperiali” till reach the Colosseum.

Timetable: 05:00am – 24:00; Night line bus 24:00 – 05:00am

Tickets:

• Tickets must be bought before boarding the bus. It is possible to buy the tickets at train stations, subways stations or at tobacco shops.
• The single ticket price (BIT) is € 1.50 and it is valid for 100 minutes. You can use it only once on the metro and use it again to take buses or regional trains.
• There are tickets that allow an unlimited number of trips in the Rome Capital area from the first stamping for 24 hours (€7.00), 48 hours (€12.50), 72 hours (€18.00), 7 days (€24.00).
• Children up to 10 years of age have free access on Atac
• Children up to 4 years of age have free access on Trenitalia
• Officilal link to check any news: https://www.atac.roma.it/biglietti-e-abbonamenti

UNDERGROUND – SUBWAY

The subway in Rome has three lines (A, B and C). The subway cannot reach the historical city center due to it is not possible to build anything underground in that area, it is too rich in history. The major tourists interest subway stations are on the subway line A: Ottaviano San Pietro (Vatican Museums), Flaminio (Popolo square), Piazza di Spagna and San Giovanni (basilica). The most interesting station of the line B are Circo Massimo and Colosseo.

Timetable:

• The Line A is active from 5.30 am to 10 pm (Friday and Saturday the service is extended until 1.30 am at night).
• The Line B is active every day (including holidays) from 5.30 am to 11.30 pm
• ATTENTION! Times often vary due to maintenance interventions. Consult the website https://www.atac.roma.it/

Tickets:

• The tickets must can be bought at train stations, subways stations or at tobacco shops.
• The single ticket price is € 1.50 and it is valid for 100 minutes. You can use it only once on the metro and use it again to take buses or regional trains.

FL – REGIONAL TRAINS

FL is the name of the Lazio railways operated by Trenitalia. It connects the city center with other roman districts and with some municipalities outside Rome. The FL5 line is useful in summer to reach some well-known seaside towns such “Santa Severa”, “Santa Marinella” and “Civitavecchia”. Other regional trains connect Rome San Pietro with Ostia, ancient Ostia, Castel Gandolfo, Tivoli and other places well known for Romans and tourists.