How To Design The Favicon
When designing your favicon use either a simple image or letters as it will be re-sized to a 16 pixels by 16 pixels icon. A design too complex won't come out clear. I usually begin by using a transparent PNG background which can be created using Gimp (It's like Photoshop but 100% free) and then place one or two letters onto the icon. I use www.favicon.cc to generate the favicon. It will convert the JPEG or PNG image into a favicon.ico file.
Favicon From Pictures
The simplest way to create a favicon is to use a simple picture and generate using favicon generators. You can use either favicon.cc or Favlcon from Pics, they both do all the hard work for you.
Once you have created your favicon, you can then proceed to uploading your favicon to your WordPress site.