Sean Earp's answer was extremely helpful, but the details were essentially off for my particular situation. Here are the steps I took to accomplish what I wanted:
- I put a copy of the favicon.ico I wanted to use in the /images/ folder by using SharePoint Designer.
- I then went into "Master Pages", right-clicked on "v4.master", hovered over "Open With", and selected "SharePoint Designer (Open as Text)".
- Then I had to find the following line within the head section:
<SharePoint:SPShortcutIcon runat="server" IconUrl="/_layouts/images/favicon.ico" __designer:Preview="<link rel="shortcut icon" href="/_layouts/images/favicon.ico" type="image/vnd.microsoft.icon" />" __designer:Values="<P N='IconUrl' T='/_layouts/images/favicon.ico' /><P N='InDesign' T='False' /><P N='ID' T='ctl10' /><P N='Page' ID='1' /><P N='TemplateControl' ID='2' /><P N='AppRelativeTemplateSourceDirectory' R='-1' />"/>
- All I had to do at this point was remove the three instances of the string
/_layouts as that would then point to the file I wanted to use.
I didn't need to insert a new <link/> line. In fact when I tried to it wouldn't use the line I inserted even though it would still show up after viewing the page's source.
All that was left was to set v4.master as the Default master page.