update:
Sample Code
It turns out that while you may be able to use the CDialogTemplate class to create your dialog, it's better to do it manually. I have written some sample code with the help of one of the developers and posted a zip file with the Visual Studio solution here.
The plugin adds a link to the left side of the case edit view "Click here" If you click it, you get a simple form. The form posts to the plugin raw page which adds an admin notification with the color and case number.
Basics
Several namespaces are available for your plugin to use. They include many of the core FogBugz UI elements:
FogCreek.FogBugz.UI.EditableTable has a full example on the plugin developers site. EditableTables come with pop-up dialogs. If you just need the dialog, you should check out FogCreek.FogBugz.UI.Dialog. The AJAX example should also be helpful. Finally, you can take a look at the source of the Project Backlog plugin to see how it creates dialogs you see when editing the backlog position. You can find it in your fogbugz folder in Plugins/examples