Newbie Permission Q

[Frank J. Schmuck]

I've installed MySQL on Redhat 7.0 from a RPM.  The install data directory
is /var/lib/mysql.  I have run mysql_install_db.  From a user account I can
run mysql and receive the mysql> prompt.  However, when I attempt something
like: mysql> create database new_db I receive the following error : "ERROR
1044 : Access denied to user: '@localhost' to database 'new_db'

I thought this might be a directory permission issue and when in as root and
change the data directory's permissions to 775 then got back in as user but
with the same result.  What am I doing wrong?

Thanks
Frank