First off, a bung is the name given to the caps used on these large barrels. And a bung wrench is a tool specially designed to tighten the bungs.
The wrenches are generally not available at local hardware stores, but can be purchased online for $7-$10 (usually) from any number of places.
Using a bung wrench is critical, as most other tools will not work for tightening a bung. Here's an image of the aftermath of me trying to use the wrong tool before I realized there was a specialized tool that would make tightening a breeze.