Creating the favicon:
1. Select your image.
2. Convert the image using a site such as http://tools.dynamicdrive.com/favicon/#.Um_uX_msh8E
3. Your favicon needs to be either 16×16 or 32×32.
4. Create the icon.
5. Download the icon to your computer.
6. Leave the name as favicon.ico
Uploading the favicon to your site:
1. Open SharePoint Designer and connect to the page you wish to add the icon to.
2. Click “All Files.”
3. Click “images.”
4. Click “Import Files.”
5. Select your favicon and click “Ok.”
Inserting the favicon into your masterpage:
1. Click “Master Pages.”
2. Check out your master page.
3. Edit your master page in advanced mode.
4. Search the code for “favicon.”
5. You should find the following code:
<SharePoint:SPShortcutIcon runat=”server” IconUrl=”/_layouts/15/images/favicon.ico?rev=23″ />
6. Change this code to:
<SharePoint:SPShortcutIcon runat=”server” IconUrl=”/images/favicon.ico” />
7. Save your changes.
8. Check in your master page and publish as major.
Checking your icon:
1. Log into your site in SharePoint 2013.
2. If the icon has not already changed, clear your cache and refresh the page.
3. If it still has not changed, reapply your page as the master page.
You should now have a shiny, or dull favicon.
Thanks to:
http://blog.blksthl.com/2013/02/26/a-guide-to-quick-sharepoint-2013-branding/
http://sureshpydi.blogspot.com/2013/06/change-favicon-image-in-sharepoint-2013.html