Can you clarify what you mean by "back up"? SQLite doesn't have a specific backup method; you have to read rows from the db and save them somehow. Many developers use XML to do this.
If the user saves the db and you then move to a new DB version code, you have to decide how you'll do the restore. Again, you have to do the work to read the backup and put it back into the database; neither SQLite nor Android does this for you.
The package android.app.backup contains classes for working with the Android Backup Agent, but they implement a general framework. It's up to you to implement the specifics for each file or database you're backing up.