download the last stable version (.tgz or .zip depending on your operative system)
Uncompress it
Copy in a route accessible via web (i.e. /var/www/...)
First time executing Lion
From a browser, open the web url corresponding to the location where you have uncompressed it (i.e. http://example.com/lion/index.html or whatever the path where you have installed lion).
A page like the following one should be shown:
Important:
If you are not able to see this page (including the images and styles) you may need to read System requirements section in order to configure your web server.
Also take a look at Troubleshooting section.
If you are able to see the page of the figure (including the images and styles), congratulations: it means that you have lion working and ready to code your own application.