Rome's other airport is Ciampino, about 20km (12mi) southeast of the city. From there you can catch a COTRAL bus that connects with a subway to Stazione Termini, or you can drive down the Via Appia Nuova.
The city bus company is ATAC, and most of the main buses terminate at the bus station outside Stazione Termini where you can get a map of the bus routes. Buses run from around 6am to 12am, with some services running throughout the night. The city's Metro service (which is convenient for many of Rome's sights) has two lines, both of which go through Termini.
A bus ticket is also valid for the city's Metro and train services. You need to buy your ticket from a tobacconist, newsstand or vending machine before you get on the train or bus - there are hefty fines for travelling without a ticket, even if you are a dumb foreigner.
The city's Metro service (which is convenient for many of Rome's sights) has two lines, both of which go through Termini. The above-ground rail network isn't much use to most visitors.
Driving in Rome is hairy in the extreme, and parking is a nightmare. Only drive if you absolutely have to.
You can pick up a cab from one of the city's many taxi ranks or phone one any time of day. Be warned though, taxis are notoriously expensive, and if you call a cab, the meter is turned on as soon as you call, rather than when you are picked up.
Sometimes, in Rome, it pays to just to get off the roads. The historic centre is relatively small and quite manageable on foot. Wear your comfortable shoes.
