You can backup the database at any time by clicking Tools and settings -> Backup now.
If you want ManicTime to make a backup automatically, you can set up Scheduled backup in "Tools and settings"-> Settings -> "Scheduled backup"
Restoring the database form a backup
In ManicTime, go to Tools -> Backup and restore -> Restore and point to ManicTimeCore.db.
What to backup?
ManicTime uses two databases, ManicTimeCore and ManicTimeReports. ManicTimeCore contains all the data you need to restore and it can be very small. ManicTimeCore is about 1/10th of the size of ManicTimeReports. ManicTimeCore will be included in every backup.
ManicTimeReports - restore will be faster. Also, if you want to import timelines form this machine on another machine via Import ManicTime timelines plugin, you need ManicTimeReports.
Screenshots - if you also want to backup screenshots.