Trip to Xi'an Airport:
It's best to take a taxi. If you negotiate, you should be able to hire one for 100-120CNY (30-45 minutes). Be clear about the terminal you're going to, as the distance between each one is considerable.
A Shuttle Bus departs from the Hotel Melody (next to Bell Tower) every 20 minutes from 6:00 to 21:00, and another departs from the train station every 30 minutes from 6:00 to 21:00. Both take an hour and cost 26CNY per person.
You can also take the public bus (Line 1). It only costs 1CNY, but we don't recommend it because the trip to the airport takes 2-3 hours!