Tickets for public transportation in Rome can be bought at tobacconists and newspaper stands, at the ATAC office on the Piazza dei Cinquecento bus square and at ticket offices in the bigger underground stations. Metro stations also have vending machines and so do some, but definitely not all, buses. Tickets cannot be bought from bus drivers.
Public Transport Tickets Rome
A normal ticket costs 1,50 Euro and is valid for 100 minutes from the moment it is used. One can take several buses or trams, but the metro only once (you can change lines as long as you stay in the system, but you can not exit and reenter with the same ticket).
The price of a 24-hour pass is 7 Euros. It needs to be validated the first time you use it, either by stamping it in one of the yellow machines in buses and trams or when entering the underground system. Upon request you need to present a valid ID. Note that this is not a 24 hour ticket. It is valid until midnight on the day you use it.
A 48-hour pass costs 12,50 Euros and the price of a 72-hour ticket is 18 Euros.
A weekly Rome transport pass is 24 Euros. The weekly pass is valid until midnight of the 7th day you use it.
All of these tickets are valid on bus, tram, metro and the Roma city trains. They are not valid for the Leonardo Express to Fiumicino or for the private bus companies that provide connections to the airport of Ciampino.
All the prices of public transport in Rome have gone up 50% in May 2012. This seems like a very steep raise, but it is not so bad once you know that there had not been any increase at all in the 10 years before that.