Do you mean that you want your user to be able to log in to a mysql database?
Mysql uses a seperate set of user accounts to the Linux login. By default, the mysql command-line tool will use the Linux username as the Mysql username (the -u option overrides this). So you need to make sure you have created a mysql account for the user.
Instructions on adding users here:
The mysqladmin tool will also help you. For details of that, type this at the BASH prompt (outside of mysql):