This is an extremely simplistic topic, but many people get stuck building their site, or one for someone else, and suddenly find this silly little file is fairly important to some people. Most annoying to me is that if I don't create a favicon.ico for each and every website I put up, I get logs of 404 errors, or a failure to find the file. Web browsers ask for this file, it seems every time they request any content from a website. It's the icon, or the small graphic that shows up in your saved favorites to mark or brand a site. It also shows up left of the URL in the address bar. It's a small and relatively insignificant image, but helps brand your site.
Creating a favicon is simple. Create an image 16X16 pixels, with a color depth of 8 bits. You can create any symmetrical image you think will look good at 16X16 and size it down. Some graphics programs do save to .ico extensions and some don't. It is a different format, so just changing the extension on a gif or jpeg won't work. There are several freely available plugins and tools that will do the job.
Irfranview is a really cool tool. It will allow you to do a lot of stuff, including mass image conversion, which can come in handy at other times. Then again, if you had twenty sites with twenty logos and wanted to kill twenty birds with one stone, Irfranview is the solution. It's batch processing could take those twenty symmetrical images and convert the size and file type for them all in seconds. However, if you just start off with the image from whatever graphics program you like, open it in Irfranview, and save it as a ico file, you have your favicon.
Adobe Photoshop and Elements, PhotoDeluxe, Corel PhotoPaint, Paint Shop Pro, Fireworks, Painter, and Photo Impact users can use a plugin from Telegraphics. It's free and open source.