There are actually some good free tutorials on PHP and MySQL available on the web, which should help you. Check out http://www.devshed.com and http://www.webmonkey.com - they both have some good ones. Webmonkey tends to be more basic and DevShed more in depth.
The problem you're having with Telnet could be that the client you downloaded doesn't do SSH - encrypted Telnet. Dreamhost requires the encryption for security reasons. See if there are any kind of SSH settings in your Telnet client, or any references to it in the manual. If not, you'll need a different program. The one I use is called NiftyTelnet, but that's just for the Mac - if you're on Windows you'll need something else. I think there are some listed in the Kbase.
One more thing - if you're going to be working much with MySQL you can save yourself a lot of headaches by installing phpMyAdmin (http://phpwizard.net/projects/phpMyAdmin/. It's a PHP script that basically puts a graphical interface on your databases so that you can enter or edit data, add or drop tables, etc. without having to muck around in the shell. It's still good to have a SSH/Telnet program just in case, and you particularly are likely to need it for troubleshooting Perl scripts if you work with those, but with MySQL, using phpMyAdmin can eliminate a lot of the need for it.