The Colosseum located 33 km from Fiumicino airport and 15 km from Ciampino airport. From both airports, the most comfortable way to reach the Colosseum will be booking of the private transfer with Sergio on Mercedes. However, if you prefer to use Roman public transportation system, the site is also easily reachable. If you want to reach the Colosseum from Fiumicino airport, the best way will be to take Leonardo Express fast train from the airport to Termini Station (ticket price is 14 euro per person) and from Termini you can use the metro system to get to the Colosseo metro stop, located right near the amphitheater. Overall, it will take around 30-40 minutes to get from Fiumicino to the Colosseum.
If you are going from Ciampino airport to the Colosseum, the best option is to take one of shuttle buses that go from the airport to Termini station. From Termini station you can easily reach the Colosseum by metro or one of the buses (64, 48, 170, 791, H) that pass Piazza Venezia. On Piazza Venezia you will see huge white marble building, the Altar of the Fatherland, behind which the Roman Forum and Colosseum are located.