Can't believe it, but yes you need a plugin to save a favicon in Photoshop. The good news is that it's free and works with all versions of Photoshop including CS5, Photoshop Elements, and Paint Shop Pro version 9 or later.
Just go to: www.telegraphics.com.au/sw/icoformat.en.html and download the right package. Then just copy the file of the package into
C:\Program Files\Adobe\Adobe Photoshop CS%version% \Plug-Ins\File Formats
restart Photoshop and there you go. Downsize your logo to 16x16px, save it as favicon.ico and upload it in the root of your website.
Most browser detect automatically that there is a favicon in the root but to be sure add
<link rel="Shortcut Icon" href="favicon.ico" type="image/x-icon" />
in the head of the website (before head tag ends).