For more option, take the special lines to Mt. Huashan from the East Square of Xian Station. The price should be RMB18.
As I know, in shoulder season, the 1st bus departs about 8:30 am ,and last 12:00 am; while in high season, the 1st 7:00 am, the last 14:00 pm.
The last returns from Huashan at the same day at 17:00 pm.

Please note the bus schedule^_^

From the Xian Airport:
The Xian Inertnational Airport is about 138 km from Mt. Huashan. With the speedway, you would only spend one and half hours to get Huashan from the airport.

From the Railway Station:
Take off at the Huanshan stop, and take public bus to the scenic area, about RMB3.
From Xian Station, there have so many special lines to Huashan. According to the type of the vehicle, the price would be RMB11, RMB16, RMB18, RMB21 respectively.

Long-Distance Bus:
At the Tangdu Bus Station (at the Langle Zhonglu) of the eastern Xian City, you can take the bus to Huayin county where Huashan lies. About every 10 minutes, one bus starts off.
Single ticket: RMB15-20.

Of course the shuttle bus is the ideal means to / from the airport, but you always should take about one hour to wait for the next one setting off if you are unfortunately miss one which is just leaving. Generally speaking, at most hotles, you can take the shuttle bus, but it is always difficult to find the hotle's exact loation near your location. With the time passing, and the flight takeoff time approaching...

So Taxi would be the best alternative. You should get to a fixed price before getting into the car. It should be RMB80 at most, and the toll (RMB5) shouldn't be paied by you.

The best way to get around is to take taxi. Taxies in Xian are not expensive and save time. The hire price is 5(or 6 for a better car)Rmb which covers the first 3 kilometres and an additional fee of 1.2/kilometres applies for additional mileages.

If you choose taxi to get to the downtown area, do remember not to take those which are waiting for hiking in queue, because you should pay more RMB 30 for parking fee as extra.
Do take those taxis who just arrive airport, pay RMB 50 they also willing to take you to city.