Rome Airport FCO to Arezzo

You can take the train, should be around 3 hours or so.

Get to Termini station in Rome and then train from there to Arezzo. There are lots of options to get to Termini from FCO. Check out RonInRome.com for more info on those.

First, you can buy your tickets from the airport train station in front of Terminal 3 to Arezzo. The fare from FCO to Rome Termini will be 14 Euro. Then, you change trains to go to Arezzo. There are two types of trains that make most of the runs during the day - the Regionale Veloche train or the Intercity train. The fare on the Regionale is currently 13.35Euro. The fare for the Intercity is currently 23Euro. The Intercity is slightly faster. The train agent will set all of this up for you. Just allow about 15 minutes in Rome Termini to change trains as the Leonardo Express from the airport comes in on track 25 which is way out at the end. It takes a small walk to get to your next train. Overall journey time should be around 3.0hrs to 3hrs15min. If you have a bit of time in Rome Termini, you can grab a bit of take away food to eat on the train. This is permitted.

I'd suggest taking the local train to Roma Tiburtina station and catching the train to Arezzo from there. Local trains run every half hour and cost EUR 8, departing from the same FCO station as the Leonardo Express. The Fast Regional trains departing from Tiburtina are just as quick as the Intercity trains departing from Termini (around 3 hours from FCO) and cost less. You can travel via Tiburtina for just over EUR 20 while the same trip via Termini could run as much as EUR 37. The change at Tiburtina is also much easier, with the walk between tracks much shorter. I've gone from FCO via Tiburtina to Cortona (a few stops before Arezzo) and it worked well. Note you'll need to tell the ticket agent you want to go via Tiburtina or they'll likely sell you tickets via Termini.

The Leonardo Express now arrives/departs from Track 24 at Termini Station, so there's a lot less walking to do - you can get off the Leonardo Express and just walk to the train for Arezzo within a minute or two.