This may not be exactly correct, spongey, but here's how I understand it:
The draft lottery is exactly that - a lottery. Balls representing each lottery participant are placed in a hopper and blown around. And then somebody, probably Stern or Granik, reaches in and reads the name of the team on the ball.
It is weighted by placing more balls in the hopper for the team with the worst overall record, theoretically giving that team the best chance of getting the first overall pick. Fewer balls are placed for the next worst team, and so on, until you have covered all of the teams, with the "best" worst team having the fewest amount of balls in the hopper, theoretically giving that team the worst chance of getting the first overall pick.
Who's on first?