Dan,
I just looked at the source code of your site homepage in my browser...it indicates your version is 1.4. You can check this by loggin in and looking in the admin area of your site....bottom of the page where you are prompted to register your site.
You can get the latest version from the download area on moodle.org here:
http://download.moodle.org/
Be sure to back-up your database and moodledata directory. When I upgrade, I use cpanel file manager and just rename my original moodle directory to something else like (moodleBAK). Then I upload the new moodle zip to the same level directory where my original exist....in your case it would be www.warrior-scholar.com and unzip the file.
This will result in the new files now being in a "moodle" directory. Then copy across your config.php and any custom themes, blocks, etc. from moodleBAK to your new moodle directory. If your moodledata directory is in your moodle directory (shouldn't be, but may be if you did an automatic install through fantastico) then you will need to copy this across as well. It is a good idea to go ahead and move moodledata outside your public_html directory if it's not already there...if you do this, just open the config.php and change the location of your datadirectory.
Also, there was a big change in the way themes are programmed between 1.4 and 1.5, so I would recommend before you start any of this, go into your admin area of your 1.4 site and change your site theme to one of the standard Moodle Themes. This should make the upgrade go smooth. Once you upgrade, then you can select your custom theme in 1.5 and see if you will need to make any changes. This probably isn't an absolutely necessary step, but it will just lessen the potential problems you may run into during the upgrade.
Visit your site in the browser and type /admin in the browser address...in your cases it would be www.warrior-scholar/moodle/admin, and you will be stepped through the process of updating your database.
I've never lost anything during an upgrade...Moodle is famous for its smooth, painless upgrades; however, it's still a good idea to back-up everything (database and moodledata directory) first. Also, I keep my moodleBAK directory until the next upgrade. That way I have all the original files in case I forgotten a hack, a theme, or whatever...the original files are still there and handy. In a worse case scenario, I could also fall back to my original site with the backup database and original codebase.
I know this may sound difficult, but it's really pretty easy once you give it a try. All the directions are in the download area of moodle.org as well.
Steve