As simple as this:
$ apt-get install mysql-common mysql-server mysql-server-5.0
a small wizard should as for a root password (for the mysql server), otherwise:
$ mysqladmin -u root -p password 'NewMysqlRootPassword'
You can create a database like this
$ mysqladmin -p create TestDatabase
and add users like this (allowing access to the just created db):
$ mysql -u root -p
Enter Password: *****
mysql> create user 'NewUser'@localhost identified by 'NewPassword';
mysql> GRANT ALL PRIVILEGES ON TestDatabase . * TO NewUser@'localhost';
mysql> FLUSH PRIVILEGES;
But, important! Keep in mind that the MySQL server is another daemon which might be vulnerable to attackers, so read this about securing the MySQL service.