All you need to do is save a small icon, sized 16 x 16, in the root folder, and call it favicon.ico.
You can also have a unique icon for individual pages. Just put this in the of the particular file, and point the URL to the location of the *.ico file you want to use:
If you are looking for a good free opensource graphics editor that works on windows, most (if not all) linux distros and more check out the gimp. Details on how to make a favicon.
A favicon.ico is one more good way to brand your website and increase recognition. Most browsers show favico.icon in their list.
It is not uncommon for webhosts to default their own favico in place of one not being there, no need to advertise for them, do so for yourself.
