Server deletion, like channel deletion, is a pretty simple process. Here goes:
1. Open up your server settings tab by clicking on the Server Name box:
2. Click 'Delete Server' at the bottom of the left hand menu, and affirm the server deletion. Boom!
Note: Only the original creator of a server has the power to delete it, regardless of the permissions assigned to any role. You'll only see the trash can icon if you created the server.