If you arrive at Fiumicino airport, you can take the Leonardo Express to arrive fast and easily at Termini Station, Rome's central station. The journey will take a little more than 30 minutes and the ticket costs €14.
Don't forget to valite your ticket, otherwise you'll get a fine. If you have a physical ticket there are machines on the platform (usually at the beginning) and if you have an online ticket from this year you need to validate it as well.
Cheaper alternatives to reach the centre are:
Take the regional train from Fiumicino airport to Termini (50 minutes, the ticket is €8, but you'll need to change train at Rome Trastevere station)
The bus is cheaper, around €6