The backup of a MySQL database over a surface like PhPMyAdmin is very simple. If you manage your database through a Unix console, you can easily create a backup using the following command:
mysqldump -u root -p --all-databases > dump.sql
If you changed the default database user when setting up the database, then root must be replaced by it. Otherwise, you could use ‘root’ standardly.
After backup file was created in the folder where you executed the mysqldump, you have the option to copy it to a local machine. Before you need to quit server connection to execute the following command locally:
scp remote_user@:remote_host/home/dump.sql /Users/local_user
Update: Since I was asked how to backup the file data of a website, the best way is to create a compressed file of your website folder executing command
tar zcvf backup.tar.gz my_website_folder/
and then download the compressed folder backup as described above.