open a favorite image that you'd like to turn into a favicon to appear in your browser's location bar
click Image→Mode→RGB
using the erase tool, erase any areas of the graphic that you'd like to be transparent
using Image→Scale, resize the image to 32×32, the proper size for a favicon
first save the file as a GIF
select * Convert to Indexed using default settings
click Export
save a copy as .ico. It will give you a number of choices for bits/pixel:
1 bpp, 1 bit alpha, 2-slot palette
4 bpp, 1 bit alpha, 16-slot palette
8 bpp, 1 bit alpha, 256-slot palette
32 bpp, 8 bit alpha, no palette
Choose 4bpp. However, I have seen with some images that 8bpp needs to be used.
upload to your website and enjoy!