The gzipping you're talking about is invisible to the end user, and for that matter, to you as a developer. It's taken care of by your web server, and the client's web browser.
For IIS, you need to enable the GZip ISAPI extension (check around on this site for a how-to), and for Apache it's mod_deflate.
When the web browser has completed its request, but before sending it out into the wide world, it will gzip the content and put a special header in, so that the browser knows the content is compressed.
When the web browser receives the response, it then unzips the data, and reads the file. This is completely transparent to the end user.
You usually only want to use GZip on text files. There's no point in using it on images, as images are already heavilly compressed.
What you would find if you watched the packets with Wireshark and re-assembled them, you would request
/index.html, but the webserver would fetch
/index.html, GZip it into
/index.html.gz and send it off. Yhe web browser knows this and unzips it so that it's back to
/index.html, so when you go to View Source you see