The first thing you want to do is create a directory below root to store your files. I say below root because then they are secure from prying eyes. Users and abusers of the web can only acces files in directories above root. So create your directory below root and make note of the server path to that directory.
Next you need SHELL access. With out SHELL access you can not do this. There are many applications out there to do this like PuTTY and others.
Then you need to log into your server using your root login. If you do not know what this is ask your host for more info.
To back up your database just type in the following line. The user entered parameters are in bold. Notice the p in front of the password.
Code:
mysqldump --opt -Q -u dbusername -pdbpassword dnname > /home/path/to/backup/dir/filename_11_16_06.sql
Change the to whatever the current date is when you back up.
When you want to restore simply change "m1ysqldump --opt -Q" to "mysql".
Code:
mysql -u dbusername -pdbpassword dnname > /home/path/to/backup/dir/filename_11_16_06.sql
It's as easy as that. I recomend that you download a copy of the file to your hard drive. This is much faster and more reliable than trying to backup and restore using a web based application like phpmyadmin. Good luck.