Brown prepared six white balls by writing numbers on them. The balls were placed in a tray with their backs to the audience. As the lottery numbers were picked on live television, Brown wrote them down on a big piece of paper so that he would not forget what they were (which is, by the way, a dead giveaway that this is a trick -- if he already had balls with the numbers on them, he wouldn't forget). When all the balls had been drawn, Brown turned around the rack with his numbers on them, revealing that his prediction was completely correct and that the lottery commission owed him millions of dollars.
But before I reveal the secret, let me dispel a number of rumors. Brown did not:
Instead the secret (and you're going to slap yourself in the head when you hear this) is that Brown filmed multiple endings to his routine -- each featuring a different prediction -- and then used computer technology to beam a different ending into each viewer's home. Most of those endings showed Brown choosing the wrong numbers, but in one home, he was seen to choose the right numbers. And in that home, the viewers were so amazed that they told all their friends, called the papers, uploaded a video of the event onto YouTube, etc. Because such a fuss was made by that one lucky family, it's their story that we all remember, giving the impression that Brown got it right.
And what about all the families that complained that they didn't see a correct prediction? Well, people just naturally assume that these complainers are sore losers, hate magicians, are Nazi-sympathizing cat beaters, or are otherwise not worth listening to.