MySql is a relational Database Management System.
Install
Install the packages mysql-server and mysql-client (which depends on the current "best" version of mysql).
MySql Server
MySql will start on boot time. You can also type manually (as root):
/etc/init.d/mysql start
After an upgrade of the Debian package you might need to run (as root):
mysql_fix_privilege_tables.
MySql will only install if you have a NON-NUMERIC hostname that is resolvable via the /etc/host file
The Debian package of MySql server creates the user debian-sys-maint that is used in the start-stop and cron scripts. Don't delete him.
MySql Client
To use MySql client just type as any user :
mysql
You can use too MySql Navigator (GUI client program for MySql database server) typing
mysql-navigator
in a terminal (the package name is the same to get it using apt or Synaptic).
or mysql-query-browser (official GUI tool to query MySql database).
After installation, you can find it in the Debian / Database menu too.
You can use too MySql Control Center, gmyclient and gnome-database .
If you have Apache and PHP installed, you can use phpMyAdmin to administer any MySql databases.