There are direct express trains from Rome to Palermo, Catania, and Siracusa. The Rome–Palermo and Rome–Siracusa trips take at least 10 hours. After Naples, the run is mostly along the coast, so try to book a window seat on the right if you're not on an overnight train. At Villa San Giovanni, in Calabria, the train is separated and loaded onto a ferryboat to cross the strait to Messina—kids will love it!
Within Sicily, main lines connect Messina, Taormina, Siracusa, and Palermo. Secondary lines are generally very slow and unreliable. The Messina–Palermo run, along the northern coast, is especially scenic. For schedules, check the website of the Italian state railway.
FS (892021 within Italy only. www.trenitalia.com.)