Someone posted some tips a few weeks ago on how to get selected for a parade. I think, more than anything, you need to be lucky. But, to increase your chances:
1) Be at the park well before it opens, particularly if you want to participate in the park opening itself. And, when I mean well before it opens, I mean at least an hour before it opens. We got to MK 45 minutes before it opened one morning - already a couple of hundred people there. And, I thought we were excited!
2) Dress in Disney-like clothes, dress similarly, or, at the very least, dress nicely. I don't mean a coat and tie, but I would be willing to bet if you're wearing "revealing" or "raunchy" clothes, you won't make the short list. As I recall, the person who started the post I referred to above was on her honeymoon. Big plus! One respondent, who was part of a group, said they all dressed alike, in homemade Disney shirts. Pretty cool.
3) Someone said they look for the "typical" family - DH, DW, DS, DD - but I don't think its a big deal.
4) Be enthusiastic while you're waiting. You don't have to lead the crowd in a sing-a-long or Mickey Mouse Club cheers, but, as you can imagine, they want happy folks.
Hope this helps. Good luck!