How you go about it depends on the type of site you have, but generically speaking your exported file should be in the '.sql' format. Again depending on your website origins, there will be an option to 'export' a backup file. The best place to download it to for ease and clarity, is your desktop. Nothing worse than a file going somewhere in the wink of an eye.
Oh yes, the prefix of the file should be something relevant. Don't go with the default filename if you have more than one database to backup.