If you have favicon.ico in your website root folder--i.e., so the favicon's URL is http://yoursite.com/favicon.ico, then you do not need to include a link to it in your HTML header. Browsers will automatically try /favicon.ico when they find no link in the header (and, some will try /favicon.ico even when do find a link in the header…).
However, if you do want to include links in your HTML header, and you can just use plain-old HTML, like:
<link rel="SHORTCUT ICON" href="/favicon.ico">
<link rel="icon" href="/favicon.ico">
Note that many browsers cache the favicon, and if they don't find it at first, they won't necessarily pick-up any code or image changes, right away. You can clear your browser cache, or try a different browser, to see the change.
I find that Chrome is actually pretty good at picking-up changed favicons.