The "Add New Group" dialog is accessed from the Groups -> New Group menu. In the dialog, type a name for the new group into the Group Name box. The shortcuts you create in this new group will be stored in a file. You can allow FastFox to give this file a default name or modify the name yourself in the Location box.
FastFox automatically creates a Group named "Default" upon installation with a few example shortcuts of different types.
You can easily change from one group to another by selecting the Groups pulldown menu. Click on the name of the group you want to use and it will be automatically loaded. NOTE: all of the shortcuts from your previous group are automatically saved.