I've read that GitLab is capable of sending messages to other servers via "web hooks" but I can't find where one would create one.
Can someone point me in the right direction?
All the answers I've found in official documentation and on Stack Overflow for finding web hooks are incorrect. The admin area > hooks page does NOT contain web hooks. It contains system hooks, which fire when you create/delete projects and users and things like that. This is not what you want.
To find your web hooks, go to the specific project > settings > web hooks (on sidebar in GitLab 6.1.0) page. These will fire on post-receive for the project in question. You can use a service like RequestBin to see what the payload looks like and to ensure you're firing these off correctly for debugging purposes.