It is possible to create a favicon online and save it to your website's root directory for later upload. Alternatively, you can use graphics software to create a favicon from an image. Don't forget Microsoft Windows users can use the 'Paint' software supplied with Windows to create favicons for free.
There are two useful pages at ixfix if you just want to get on and create your own favicon. Go to the favicons generators page for instant results at one of the many free online favicons generators. Visit the ixfix free favicons software page if you would rather download software to your hard drive and control the favicon creation process. I only list free favicons generators and free favicons software at ixfix.
Free Graphics Software - Free Graphics Software - This page list various free graphic programs that will mostly all manage to create favicons as well as other graphics files. The software is freeware or open source.