I would strongly suggest that everybody learn how to do a backup themselves. I've seen many users get screwed when they did something, then wanted a backup, but the backup their host provided was corrupted (of course, then they blame it all on their host when it is really their own fault for not making sure there was a good backup). Learn to do a backup yourself and how to import a backup into a new database yourself. Do this *before* you absolutely need to do it (when your site is down). The time to learn is when you have the time, not when you are in a panic. I think it's great that the OP is already looking into this.
From the manual:
Backing Up The Database via SSH/Telnet or
Backing Up The Database via phpMyAdmin
Restoring The Database via SSH/Telnet or
Restoring The Database via phpMyAdmin
If you don't have shell access, some people have also reported success with these scripts:
MySQLDumper
MySQLHotxcopy
Bigdump