To confirm what has been written with some more detail:

No need to ask gate agents. In terminal C, head to gate 39 and there will be transport agents wearing yellow vests tasked to transport passengers from terminal C to terminal D. You will arrive within 10 feet of the Admirals Club in terminal D, passing by transport agents that will be available for when you are ready to return. No need to pre-schedule. It seems as though there are at least 2 shuttle buses running along this route. Once you ask to be shuttled, they will call for a bus and guide you onto it once it arrives (if not there already).
However, do keep in mind that there could be a few minutes worth of wait if both buses are in the middle of a transit.
In my experience, they did not wait for extra passengers to fill up the shuttle. I was alone on both rides (C->D->C). Awesome service btw. Hope this helps.