To create a new database:

$ mysqladmin create <database_name>

To grant permissions to a user, run this:

$ mysql -u root -p
Password: (enter password)
mysql> GRANT ALL ON db_name.* TO username@localhost IDENTIFIED BY "userpasswd";

To flush the privilege tables, run this:

$ mysqladmin flush-privileges

or:

mysql> flush privileges;

To revoke the privileges from a particular user/host pair:

mysql> revoke all privileges, grant option from username;