You don’t say, but I’ll assume you’re asking about XML.
Look at the 3.0 StateCharter sample. At the top of InitReaderWriter, it sets up a GoXmlBindingTransformer for the StateChartDocument, and saves some "global" settings like version and path. This is probably where you want to save things like BackColor and BackgroundImage.
Tooltip text is probably a property of your links or nodes though, and you should save that with them, if in fact the tooltips are different for different objects.
Now, to confuse the issue a bit... some settings in an application may be "user preference", and shouldn't be saved with the documents. I could imagine "Background color" might be one of these for some applications. How user preference settings are saved is outside the scope of GoDiagram, but .NET has some support for application configuration files.