There are three ways you can do this:
1. Use phpMyAdmin like another person said above
2. Use MySQLFront (I personally love this program because you can connect to any remote MySQL database and do anything that phpMyAdmin has as well, you'll just have to write some of the queries yourself)
3. If you have access to run the mysql command from a command line Here is the command you want to use:
GRANT ALL PRIVILEGES ON [database].[table] TO [username]@[host] IDENTIFIED BY 'some_pass' [WITH GRANT OPTION];
The items in [] need to be filled in, or are optional.
[database] : name of database that you want this user to access. They will only have access to this database. You may let them access every database by simply using *
[table] : same type of access structure as database above, whatever tables you list here are the only tables they can access. if you have defined * to be the databases they can access, make this *
[username] : username that user will use to connect
[host] : host from which they will connecting from, this can be a defined host, or can be a wildcard in which case you would use %
some_pass : choose a password for that user to use to connect
[WITH GRANT OPTION] : if you want this user to have access to the mysql.user table simply add this comment. if you leave it out, they cannot modify the mysql.user table. this is a good security measure. I would leave this out, unless you really trust the user that is connecting to your database.
I apologize if any of this doesn't sound right or if i'm mistaken on any part. I'm going off the top of my head on this. If you want detailed information visit:
http://www.mysql.com/doc/en/Adding_users.html