Hi,
I'll try to explain you the steps you need to do to get the db backed up in shell and ready for download.
1. Ssh to the server as root using these instructions:
http://www.lunarforums.com/lunarpages_dedicated_web_hosting/how_to_login_to_your_dedicated_server_via_ssh-t26372.0.html2. Run
mysqldump -u admin -p`cat /etc/psa/.psa.shadow` [db_name] | gzip > /var/www/vhosts/[domain_name]/httpdocs/[db_name].sql.gz
(replace [db_name] and [domain_name] with actual names)
3. Download the file by opening http://[domain_name]/[db_name].sql.gz in browser. You should be able to open it in any archivator supporting ZIP archives on your PC in case it is needed.
Please advise, if something is still unclear for you.