There are a couple of direct trains to and from Xi’an-Huashan & Luoyang-Huashan every day (see the timetable below for details).
From the train station at Huashan village, buses go to the start of the route for RMB5, or alternatively you can get there with a twenty-minute walk (head south to the bottom of the road, turn right on to the main road, and take the next road on the right to the “entrance”).