The Leonardo Express is the name of the train that'll shuttle you from Rome's main international airport, Fiumicino, to central Rome's Termini station.
A Leonardo Express train leaves every half hour in each direction.
From Rome Termini: Trains to the airport start at 5:52 in the morning, with trains running at 22 and 52 minutes after the hour. The last train of the day departs at 22.52 (10:52pm).
From Rome's Fiumicino International Airport: Trains to Termini Station start at 6:35 in the morning, with trains running at 5 and 35 minutes after the hour. The last train of the day departs at 23.35 (11:37pm).