Umpire Interference

Despite its having six rules references, umpire interference is pretty straightforward, having just three scenarios:

If an umpire on the bases is touched by a batted ball before the ball touches or passes an infielder (except the pitcher – just ignore the pitcher for now), you have umpire interference. In general, we're talking about the umpire getting hit while positioned in the infield.
If an umpire on the bases is touched by a batted ball after the ball touches or passes an infielder (again, except the pitcher) you have nothing – live ball, play on. In this case, the umpire is positioned behind the infielders.
If the plate umpire impedes the catcher's throw to attempt to retire a runner advancing, you have another flavor of umpire interference. This normally occurs with a runner stealing, or advancing on a wild pitch or passed ball.

You handle each of these cases differently.

1. Umpire touched by batted ball before passing infielder

In the case where an umpire is touched by a batted ball before the ball touches or passes an infielder, call interference on yourself immediately. Call "Time! That's interference!"

Award the batter-runner first base.
Other runners advance if forced. (Your partner is laughing by now. Do what you can to recover your dignity and move on.)

Important: If the ball touches the pitcher before touching the umpire in this scenario, then you do not have umpire interference. Live ball. Play on.

2. Umpire touched by batted ball after passing infielder

In the second case, where an umpire is touched by a batted ball after it has passed or was touched by an infielder (again, not the pitcher), do nothing. This is a live ball. Play on.

3. Plate umpire impedes catcher's throw

If you are the plate umpire and, on a steal, you inadvertently bump the catcher or otherwise impede his ability to make a play on the runner, call "Time! That's interference."

The ball is dead.
Any runners moving on the play must return to their original base. (Your partner is laughing on this one, too.)

In all other situations where an umpire inadvertently contacts a base runner, a defensive player, or the ball itself, you have nothing. Live ball. Do what you can to minimize your impact and let play continue.