How do we get from Luoyang to Pingyao and back,

There is one ordinary train available. The train departs from Luoyang Raiway Station at 05:54, and the trip takes about 11 hours.
Or, you may take a bullet train to Xian (about 1.5 hours) to have a visit. Then, take a bullet train to the place (about 3 hours).
Another way is taking a normal train to Taiyuan first (there are three per day), then change to a bullet or normal train to the final destination. You can get the train schedule on this website.
By the way, there is no direct bus to the place. ;)