Far and away the best method to use, no matter what your level of experience, is Fantastico... Most cPanel server accounts will offer you this option. Here's a low-priced hosting account option which will get you operating online very quickly. It includes Fantastico. Click here to learn more about using Fantastico to install your Joomla! site.
Then there's the Joomla Desktop Installer, you can use this to install a remote copy (to your Web Hosting Account) or on your local server. It still requires that you run the Joomla! installer afterwards, unlike Fantastico. (Do not choose the version for Joomla 1.0 - only 1.5)
Thirdly, a manual install. Download Joomla!, upload to your hosting account, unzip and then go through the Joomla! installer process. (After unzipping, go to the install location on your site). Go here for a fuller rundown on how to do a manual installation of Joomla!
