After getting your favicon, you'll need to login to your website using your preferred FTP Program. Once you login, go to /httpdocs/ and find a file named favicon.ico, and delete it. Now upload your favicon.ico in that folder and you're done !
Just wanted to add to this, it is important that you choose an image that is representative of your site (logos always work), but it should be something that is legible to the viewer. A sophisticated graphic will be deemed useless.
It seems like a minor thing to update your favicon, but it does play an impact on people's perception of your site. It can make it seem much more professional and interesting.
Great add, it's also good because many people bookmark sites, so when viewing list of sites bookmarked your site will standout a little more with the right icon.