You need to download the Photoshop icon plug-in to make an actual .ico file type
Once you have the plug-in installed, .ico becomes an option when you save.
You don't actually need to use any kind of link in your <head> section. Simply placing the .ico file in your site's root folder is enough. If the OCD kicks in and won't allow you to leave an image floating out there next to your index.html, you can put it in an image folder and add the link to your head section.