Saving the database
When you quit Frontier, the database is saved automatically. (This is a change from previous versions.)
You can save at anytime while you use Frontier by pressing (Cmd) [Ctrl] -S or selecting the "File -> Save Database" menu item.
If you don't want to save the root when you close it, while holding down the shift key, click the close box on the Frontier.root window. This will close the database without saving it. (Clicking the close box alone usually just hides the database window.)
Holding down the shift key while you quit Frontier will also prevent the save. The application will also exit.
If you prefer to have a dialog box come up, asking if you'd like to save, you can set a preference for it. In your user.prefs table, create a boolean item called "autosave" and set it to false.

Backing Up the Database
You should back up your database on a regular basis! You never know what is going to happen.
You can backup at anytime while you use Frontier by pressing (Cmd) [Ctrl] -B or selecting the "Main -> Backup" menu item. It's at the very bottom of the menu.
If you leave your machine and Frontier running all the time, you can set Frontier to basckup every night. You'll have to use Frontier's builtin scheduler for this. From the Main Menu, choose the "Scheduler -> Add an Overnight Task..." item. A dialog box will ask you to:

Then enter "backups.backuproot ()", without the quotes. You're done, and if Frontier is running, it will back up at midnight. You can edit the location of the backups at user.backups.folder. It defaults to a backups folder in the main Frontier folder.
Save a Copy
Occasionally, the database will need to be compacted down. If you notice that it takes a long time for Frontier to save the root when it shuts down, you should save a copy of the root.
Choose "Save A Copy..." from the File menu to save a compacted root file. Give the copy a name, like "Frontier.root.fresh". (Don't save directly over the old Frontier.root file, this could cause corruption.) Quit Frontier. Trash or store your old Frontier.root file elsewhere, rename the fresh copy to "Frontier.root" and then restart Frontier. Your database is now faster and more compact!

TIP: To see a display of the internal statistic on the database, open the Quick Script window, and type: window.dbstats ().
Scripting.com has a page about Save A Copy. Although it's part of the Frontier 4 site, the information is still relevant. Take a look:
http://www.scripting.com/frontier/snippets/saveACopy.html
The end!
Great, you're at the end of this little tour of the database. In less than 1/2 an hour, you've become aquainted with the "workshop" environment of Frontier. Congratulations!
I know you're just dying to read more--lucky for you, there's the tech note!
Page 1: Frontier's Database Defined
Page 2: The Advantages of Frontier's Database
Page 3: What's in the root?
Page 4: Navigating the Root
Page 5: Where do I keep my stuff?
Page 6: Database Names and Addresses
Page 7: Database Care and Feeding
Page 8: Object Database Tech Notes