When Handy Address Book is running it places this icon: in your system tray  The system tray is normally in the lower right portion of your screen.  You can left click on this icon to restore Handy when it is hidden.  Handy is hidden whenever the "close" button in the upper right corner of its window is clicked, or when choosing File/Hide to Tray.

To access some commonly used commands without re-opening Handy, you can right mouse click on the icon to pop up a menu, as shown here: