You save a diagram by either using the File | Save or File | Save As menu commands, or you can use the ⌘+S or ⌘+⇧+S keyboard shortcut combinations. The save or save as dialog is the standard Macintosh one, thus you should feel quite at home.
Confusingly, on the Macintosh a file might really be a folder. A good example of this behavior is the Application folder. The "applications" (like OmniGraffle) are really a folder on their own with a special file structure. In these folders you will find a lot of supporting files and directories.
This collection of files is called a bundle. For applications we have Application bundles—and data saved by an application is called a file bundle.
OmniGraffle might store your diagram in a file bundle. ...