You put a filter sponge that has been sitting in your sump or overflow as it will be stuffed with beneficial bacteria, that is your substitute for rock and sand. The sponge and bacteria filter the water. I also add a bacteria additive to help the process just in case. (I am not writing well tonight, been a long week).
To put things a bit more simply I hope, here is what I do. I put sponges for the aquaclear filters in my sump for 2+ months (I just leave them in there all the time). When it comes time to QT you fill the tank with DT water if possible, put the sponge in the filter. Start running the tank as normal (heater, powerhead, filter). Add some bacteria if you feel it is neccesary. I keep an ammonia alert badge in my QT as well. No sand or rock. Just PVC or plastic decor.