Download the last stable version (.tgz or .zip depending on your operative system).
Uncompress the file downloaded.
Copy to a location that is accessible via your web server (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 path for which 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 you are ready to code your own application.