This is a question we get all the time! For those of you that may be unfamiliar with the story, when Magic Kingdom opens, the train comes into the station at the Magic Kingdom gate with all of your favorite Disney characters; Mickey and Minnie Mouse, Donald Duck, Goofy, Pluto, and so on. As part of this entourage, one family gets to "help" open the Magic Kingdom. You ride in on the train with the characters, throw confetti, and so on. Sometimes, you get to open Mickey's Toon Town Fair, the Tea Cups, ride in the parade, etc. It really depends on the day, whether you have kids or not, and lots of other things.
More importantly, how do you become "that" family? One of my favorite answers is 50% luck and 50% magic. 
In truth, luck has a lot to do with which family is selected, but there are some things you can do to sway the odds in your favor.
- Arrive EARLY! By early, I'm talking 2-3 hours before the park opens. Your goal is to be the first family at the gate.
- Be enthusiastic! I know this can be very tough when the kids are up early and cranky and tugging at your leg, whining for a bathroom and so on. However, Disney wants happy families to open the Magic Kingdom, not stressed, frustrated parents.
- DO NOT bother when Extra Magic Hours occurs in the morning at Magic Kingdom. They don't have the ceremony, so you'd be wasting your time.
You can also try to be "pre-selected" to be the Magic Kingdom opening family. Remember, I said "try." Disney and the Magic Kingdom insist that the selection process is completely random and that you cannot "request" to be the opening family. However, we've known several people that did get "pre-selected." So, how did they do it? All of them did it the night before the day they wanted to be the Magic Kingdom opening family. Your best bet is to talk to one of the gate or guest services managers and have a story.
What do I mean by have a story? Your grandparents are with you and celebrating their 60th wedding anniversary, you have a terminally ill child, you just got back from the Olympics where you won a medal, you saved money for 40 years to make this trip to the Magic Kingdom. You get the idea. Add some spice, adventure, or emotion to why they should "pre-select" you.
As I noted, this is a long-shot, as we've been told repeatedly (even when we've tried the above tactics) that you cannot be pre-selected. However, we've known too many people that have been pre-selected to realize that this just isn't true.
Your best bet is just to arrive early and look like the biggest, most enthusiastic Disney fan you've ever seen.
Good luck!
Here's a video from the selected family perspective:
Tomorrow: Disney parades and shows.