If you have telnet/SSH access then you can do something like:
mysqldump --user {dbase_username} --password={password}{dbase_name} > {full_path_to_sql_backup_file}
Just replace each { } bit with the appropriate data then download the backup file at the end of it - warning, this can be quite big. As to how you reimport the data, maybe have a look on Google for mysqldump as I've forgotten the command for this.
Alternatively you could use PHPmyAdmin from:
http://www.phpwizard.net/projects/phpMyAdmin/
This provides a more friendly front end to the whole process, just go to export > data & structure > select the tables > select all the tick boxes and download the text file when asked. If its a large database you might want to export each table one at a time to avoid timeouts.
Its also worth checking the text file afterwards just to make sure it hasn't truncated part way through the export process.
This also provides an easy way to import the data just going to import and selecting the text file(s) that you created above.
Trev
http://www.aardvarktravel.net
