The ‘WordPress’ way of adding a favicon to your wordpress site is to upload the favicon.ico (16×16 pixel jpg, gif or pgn) to the current theme main folder and the main directory of your site using ftp.
This methode works well for internet explorer but somehow my recent version of chrome does not show the favicon.
On the wordpress site they state that this is the case in some ‘older browsers’.. strange.
To fix that you can add some code to the header file, check the source (didn’t workout for me however)
Best tip: Forget all of the above!
Just use this plugin: All in one Favicon, it works (still) great, you can even specify seperate favicons for front and back end! Install plugin and upload the image you like and your done.