If you are specifically looking for adding the favicon in asp.net site refer this link:
FAVICON Asp.Net[
^]
<link runat="server" rel="shortcut icon" href="~/favicon.ico" type="image/x-icon" />
<link runat="server" rel="icon" href="~/favicon.ico" type="image/ico" />
Adding both these tags would help work in both IE and FF.