One must use Regedit for such things. Run (WinKey + R) Regedit and navigate to HKEY_CLASSES_ROOT\Directory\Background\shell. Under shell create a new key with a miscellaneous name (e.g. Fire1) and set its value (in the right pane) to the name you wish the item to have (e.g. Firefox.) Then create a new key under it, named command, and this time set its value to the exact path of the target executable. Remember to experiment.
The result:
To set some of the items in that image, it is a little more complicated. I would recommend you query these individually. To add the control panel for example, one would create the following structure: HKEY_CLASSES_ROOT\Directory\Background\shell\Control Panel\command and set command's value to rundll32.exe shell32.dll,Control_RunDLL. For more information see the following tutorial I just found.
I believe there is a freeware program called FileMenu Tools that has a comfortable interface to modify and customize the context menu for explorer and perhaps some other interfaces.
