The posts that I have read from those that were selected to be Grand Marshal's in the parade at MK(I'm assuming that's what you're asking about), all have said that they (the family) were asked to participate by a CM near the beginning of Main Street. Some people posted that they were wearing their ears and homemade Disney shirts. Some people posted that they were overheard talking about their excitement/love of WDW. And others posted that they had no idea why they were asked: they probably just had a certain "look" that the CM was watching for. Every post that I can recall all said that they were there at opening, or just a few minutes after, when they were approached. They were told to be at a certain place at a certain time. Of course, if you're in the beginning of the parade, you're probably going to miss quite alot of it. If you have cameras or camcorders, there are CM's who will take your pictures/video with your family in the parade, with your own cameras.
Obviously, not everyone who has been a Grand Marshal has posted ther're experience. I remember about 4 posts from people who were picked, and they all pretty much described the same experience. They all were families, with 2-3 kids. Whether or not they always pick families, I wouldn't know, because I haven't seen every parade. If there are other spots in MK where they ask people to be Grand Marshal's and other times they do it, I haven't heard of any. I remember the last time we went, they had two separate families in the parade.
I have never read any posts by someone who was picked at another park other than MK, so maybe someone has more info on the other parks.
Good luck on trying to be picked - hope it happens!