We've never been fortunate enough to nab this, but from what I've read the family is picked right at park opening, as guests are first coming in, on the main street. Generally it seems a family is targeted, although honeymooning couples in the ears also have reported success. The families I remember reading about tend to be wearing matching shirts, or all Disney-related things, or are simply poster children of the happiest place on earth. I remember one report of getting asked after being seen skipping arm in arm down the street having fun. I remember another person reporting that an early PS into a park before opening got them an invitation to be Grand Marshalls at MK as they were strolling down Main Street back to the front gates before opening.