I have received mixed reviews on plumbing a dishwasher w/o a vacuum breaker/ air gap. I would like to have someone explain in detail how it would work w/o. I do not have a hole in my sink for one.

You do not have to have an air gap. Just loop the drain hose up to the under side of the counter top and secure with a clamp or the like and bring it back down to the drain or disposal and connect. That eliminates the need for drilling hole in counter top for air gap and serves the same purpose