A simple VOR DME approach is nothing more than a regular VOR approach in which a DME fix is necessary along the final approach path to define when the pilot may begin a descent to a lower specified altitude.
A more complex VOR DME approach is one in which the DME must be used to fly an arc to arrive at a postion where the pilot can turn to his/her final approach course. This is often used in cases where there is high terrain that would interfere with a long final approach course. In that case, the published approach would call for approaching the airport from one side or the other, once reaching a measured distance from the DME, flying an arc toward the final approach path maintaining the stated distance from the DME, then turning onto the final approach path once you reach it. For an example, you can go to airnav.com and download the VOR/DME Rwy 34 approach at St. George, Utah (SGU).
In either case, in order to execute a VOR DME approach, the aircraft must be equipped with a DME and it must be used during the approach.
VOR DME arcs are among the most difficult skills a new IFR pilot must master and, unfortunately, there are not very many such approaches so it is hard to maintain that skill. This is one of the uses I have for FS9. When I maintain my competency at such manuevers in FS9, it makes it easier for me to maintain the same skill in the aircraft.