From this source.

How do I manually add a user to my database?

You can add users two different ways: by using GRANT statements or by manipulating the MySQL grant tables directly. The preferred method is to use GRANT statements, because they are more concise and less error-prone.

There are also several contributed programs (such as phpMyAdmin) that can be used to create and administer users.

The following examples show how to use the mysql client to set up new users. These examples assume that privileges are set up according to the defaults described in the previous section. This means that to make changes, you must be on the same machine where mysqld is running, you must connect as the MySQL root user, and the root user must have the INSERT privilege for the mysql database and the RELOAD administrative privilege. Also, if you have changed the root user password, you must specify it for the mysql commands here.

First, use the mysql program to connect to the server as the MySQL root user:

shell> mysql --user=root mysql

Then you can add new users by issuing GRANT statements:

mysql> GRANT ALL PRIVILEGES ON *.* TO [email protected]
mysql> GRANT ALL PRIVILEGES ON *.* TO [email protected]'%'
mysql> GRANT RELOAD,PROCESS ON *.* TO [email protected];
mysql> GRANT USAGE ON *.* TO [email protected];

monty A full superuser who can connect to the server from anywhere, but who must use a password 'some_pass' to do so. Note that we must issue GRANT statements for both [email protected] and [email protected]"%". If we don't add the entry with localhost, the anonymous user entry for localhost that is created by mysql_install_db takes precedence when we connect from the local host, because it has a more specific Host field value and thus comes earlier in the user table sort order.
admin A user who can connect from localhost without a password and who is granted the RELOAD and PROCESS administrative privileges. This allows the user to execute the mysqladmin reload, mysqladmin refresh, and mysqladmin flush-* commands, as well as mysqladmin processlist . No database-level privileges are granted. (They can be granted later by issuing additional GRANT statements.)
dummy A user who can connect without a password, but only from the local host. No privileges are granted--the USAGE privilege type allows you to create a user with no privileges. It has the effect of setting all the global privileges to 'N'. It is assumed that you will grant specific privileges to the account later.

The other method os manually manipulating the user table is outlined in the link above but not recommended.