From Joomla! Documentation
Before you can begin using Joomla! you will need a working installation of Joomla! If you want your site to be available on the Internet, make sure that you have an account on a web server. For most people this means signing up with a hosting company and purchasing a domain that will serve as your site's main address.
- Want to build a free Joomla! website? launch.joomla.org is a Joomla! service that allows you to start, build and maintain a completely free website on a joomla.com subdomain for an unlimited time. The site building software features all of the Joomla! CMS core functionalities that make building a website easy and flexible.
- Already have a hosting company? Joomla! is offered by most hosting companies under "One Click Installs" (also called Auto Installers) for their customers. The "One Click Install" method offers an "instant" installation of Joomla! which is quick and easy. Follow the instructions your host provides.
- Use the conventional method of installation. This requires you to copy the Joomla! zip file to your hosting account, unzip, create a database, and then run the installation. Complete instructions can be found at Installing Joomla. Further information can be found at Joomla! Installation Resources.
- Install Joomla! on your own computer (without your site appearing on the Internet), you can install it using the XAMPP package. Install XAMPP and then use the "conventional method" to get your Joomla! test site working.