to change your root mysql password, do the following:
% mysqladmin -u root password <your-desired-password>
that will set the root password,,,
now, to add a new user:
% mysql -u root -p
<type your password>
mysql> GRANT ALL on <databasename or *>.<tables or *> TO <username>@<hostname (try localhost)> IDENTIFIED BY "<password>";
if you want the user to be able to grant other users access, append WITH GRANT OPTION to the end of the last command.
*'s above represent wildcards.