It does not work with clipboard, you need to have the actual .ico file saved on your computer.
If you want to set the default favicon for your (that means you are the author) web pages, the instructions are here.
If you just want to customize the icons in your favorites pane or menu, then right-click on the item in the favorites pane in Internet Exporer and then click the "Properties" command. Finally click "Change icon" button on the property page and navigate to the saved icon.
I am not sure whether it is possible to customize favicon if you are using Firefox.