Creating a Cut-Out Effect for Bitmaps

Introduction

I've been trying to figure out how people do this effect in their Flash movies for a long time. When I finally got it, I bounced my head off of the floor for a few days. It's so simple that it only requires two pieces:

1. An image (preferably a bitmap because Flash compresses it better than jpegs or gif images.
2. A vector to trace the shape you want removed