Rome has three metro lines (A to C) and an extensive network of city buses you can use for these. You have several options for buying tickets at the ticket machines at the metro and bus stations and at tobacco and newspaper shops. It is important to know that the same ticket is valid for all public transport (ATAC) including metro, trams, buses (with the exception of the tourist buses) and even a number of regional trains. These tickets are not valid all the way to the airport.

Do remember to stamp your ticket (you do this yourself in the buses and trams), or you will risk a fine.

You can choose from a number of different tickets here
Detailed routes can be found here