You'd want to design a small icon (like 16x16) with no more than 24-bit color depth (although I'm not 100% sure that's the max color depth). Then you'd save it as an icon (.ico) and upload it to the root directory of your site (so public_html or www or httpdocs or htdocs).
Then just refresh your browser. You're also able to define where your "Shortcut Icon" is with a <link> tag in the head of your HTML page.
Wikipedia Page <-- See that page for specifications and good information.