If you need to get from Ostia to the Airport, you can catch a local bus from the Central Metro station; cost 1.2 euros. Runs every 20 min or so and takes about half an hour . It stops at several locations at the airport including the main terminal. Look for the blue bus to the left as you come out of the metro station.
If you need to get to the Central Metro station from other stops in Ostia, the metro is 1.0 euro and runs every 15 min in the morning.