I completed my first installation of XAMPP Server and down load of Joomla 1.5.9. Therefore, I able to log-in as administrator and begin to build a website on my stand-alone computer. I wish create another website. Where do I begin? Do I have download another copy of Joomla unzipped into a sub-folder? I assume I do not have reload XAMPP. Please advise. Thanks

You should not need another installation of xampp, in fact I am not sure if you even could install it twice. XAMPP simulates a web server, you could run as many websites on it as you want, you just don't get seperate domains for each.

Just make a new folder, unzip joomla to the new folder. Make a seperate database for the second install. Go to your localserver address with a /secondsite folder and you should be able to complete the install.