Try the WordPress Database Backup plugin.
Just install from plugins and it seems to work pretty well. Creates either a download file or you can email the resulting file or keep it on your hosting.
Although I can't vouch for how good it is at restoring yet as I havent had to do.
You will also need to backup your site (all the html, php files etc) and you can do this simply by copying it all to your local machine via ftp. There are probably other ways of doing that though.
But I think your topic referred to the actual database. Hope that helps.
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