Depending on the kind of public transportation that you will be using and the length of your stay in Rome, you can buy different kinds of tickets.
The BIT ticket has a duration of 75 minutes from its validation and allows unlimited changes between different forms of transportation. The only limitation is to leave and to enter again by the metro turnstiles. The price is €1.
The BIG ticket allows unlimited public transportation from the moment of validation to midnight of the same day. The price is €4.
This pass gives you unlimited use of the public transportation for the day of validation and the following two days. The price is €11.
Similar to the previous card but with a validity of 7 days. The price is €16.
If your stay in Rome is for a longer period, there are also annual and monthly travel cards.
Public transportation tickets can be bought in the metro machines, corner shops and news stands. There is also a way to buy tickets by SMS, but is not good value unless you have an Italian mobile phone.