When the application is first installed it will be docked to the right side of the screen. As such, if you move the mouse to the right edge of your screen it will popup after 1 second.
Once you move the mouse away from the AstoundingDock it will hide again.
To add an application to the AstoundingDock you can just drag over to the right side of the screen, once the AstoundingDock poups up you can drop the application into the "General" section.
You can see here that I've dragged the "Google Chrome" shortcut from the desktop into the "General" section of the AstoundingDock.
You can run "Google Chrome" by left clicking on the icon.
Right clicking on the "Google Chrome" icon brings up the standard context menu with additional "Edit Dock Entry" and "Remove Dock Entry" items.
For more details on how to use the AstoundingDock see the Help page.