For a little while there, WP-DB-Backup was bundled in with the core of WordPress, and I have no idea why they took it out, because no WordPress installation should be without it. If you lose your WordPress database, you’re screwed. And you may hope that your hosting company is backing it up, but are you sure? Besides, with all those hackers out there eagerly seeking out vulnerabilities in WordPress, it’s a good thing to have a copy or two or three of your database around.
Once you’ve installed and activated the plugin, you’ll see an entry for “Backup” under “Tools” in your dashboard. You then have the option to make an immediate backup (always a good idea) and to schedule backups (an even better idea). Unless you are a rabid fiend of a blogger or run a site with multiple contributors posting several times daily, a weekly backup is probably sufficient. (If I can post something new to all of my blogs every week, I’m doing well.)
The backup comes as a .tar.gz file. Just save it on your computer. In most cases, these files aren’t very large, so you can keep several weeks’ worth without any problems.
If you need to use it, you’ll have to go in through the PHP MyAdmin panel and upload it through your file manager or by FTP. This is only moderately scary, even for someone who doesn’t know much about these things. There are some guidelines in the Codex about it. I followed them and they worked.
I have a longer post about backing up WordPress over on the FileSlinger Backup Blog.