By fast train, it takes about 3 hours to go from Lanzhou West Train Station (Lanzhouxi) to Zhangye West Train Station (Zhangyexi).
Here are the instructions:
1) To go to Lanzhou West Train Station, Bus 31 can be caught on Zhongshan Rd, 50 m south of the Pedestrian Street, on the West (left) side of the street, see attached map. The train station is the last stop for Bus 31 going west.
2) Advance tickets can be purchased online, for example on Trip.com (formerly Ctrip), but they still have to be picked up at the ticket counter.
3) The fast train arrives at Zhangye West Train Station (Zhangyexi) which is on the edge of the city. The bus stop is right outside the train station, about 50 m from the exit, just follow the crowd. Bus 22 (costs 2 CNY) goes to the center of Zhangye and passes near the Drum and Bell Tower which is the geographic center of the city. Bus 1 (the blue one, not the green one) also leaves from the train station.
There are also plenty of taxis that will go to the center of the city for about 10 CNY. The price is cheap but they will give the hard sell for tours to the Danxia Geological Park.
4) To return to the Zhangye West Train Station, Bus 22 goes roughly along the same path in the opposite direction. The train station is the last stop.