The old way, simple but now being phased out, is GKSu. Here is the discussion on GKSu's future.
The new way is to use PolicyKit. I'm not quite sure how this works but I think you need to launch your app using the pkexec command.
UPDATE:
Looking at the example code on http://hal.freedesktop.org/docs/polkit/polkit-apps.html, it seems that you can use PolicyKit to obtain authorization for certain actions which are described by .policy files in /usr/share/polkit-1/actions. The action for executing a program as another user is org.freedesktop.policykit.exec. I can't seem to find an action for directly accessing block devices, but I have to admit, the PolicyKit documentation breaks my brain too.
So, perhaps the simplest course of action for you is to separate your disk-mangling code that requires privileges into a command-line utility, and run that from your GUI application using g_spawn_[a]sync() with pkexec. That way you wouldn't have to bother with requesting actions and that sort of thing. It's probably bad practice anyway to run your whole GUI application as root.
Another suggestion is to ask the author of PolicyKit (David Zeuthen) directly. Or try posting your question to the gtk-app-devel list.