where to find mysql accounts on root

I have such problem:
The serwer I had my accounts is offline and my admin gave me the HDD to copy my accounts from it.

I'ma a newb and it's simple when it comes to copying accounts from /home/ but I have problem how to copy my databases to another provider's server.

I can't find nowhere *.sql files. I've only found database names in home/mysql but inside the table names have strange (for me) extensions.

Can anyone tell me how to copy mysql databases from this disk to *.sql files so I can put it somewhere else?

*.sql files are just dumps, so either use phpmyadmin or (via ssh) mysqldump to dump all databases......

You can also copy the /var/lib/mysql/
and put them back on other server (before restoring, mysqld stop, restore files, chown mysql:mysql /var/lib/mysql -R and then mysqld start)

in Debian mysql data stored in '/home/mysql/'