I am just starting out with Linux and have now installed MySql on it. I can log into the MySQL, but now I want to add a user which can access the MySql server from several different locations.

This is what I have tried at the MYSQL prompt and keep getting an sql error on:
Any ideas?

Thanks, Chester

you need to quote strings, such as the username.
Try:
GRANT ALL PRIVILEGES ON *.* TO 'myUser'@% INDENTIFIED
BY 'myPassword';

That did the trick, but I am still not able to log into mySQL server externally. When it is on a Windows box, all i need is the Host name of the box MySql is on, a user and password for mysql. When I try it with MySql on Linux, I get an error of host not found. I checked the hostname of the Linux box and it is correct. I read something about that I may need to enable SSH tunneling or something on the Linux box to allow external connections, what is that all about and how would I accomplish that? Any ideas of how I can connect externally would eb appreciated.
Thanks, Chester

Depending on your server version and the version the client is using you may be affected by this:
http://dev.mysql.com/doc/mysql/en/old-client.html
Basically the mysql dev team changed the default password format to something more secure in the latest release. This, unfortunately, broke many legacy (and some not-so-legacy) clients. There are instructions on how to work around the issue on that page.

Things will get very easy if you install webmin, goto MySQL server and change user permission -> host any