There are 2 ways to set your favicon on any website. One is through html link tag, other by putting .ico file in your root directory. Setting with html will overwrite the .ico in your root directory in case you set them both.
To define favicon with html tag:
You can use any png, gif, jpg file as icon and define it in your html header, between <head> tags. You can use animated gif as well.
This will be used for all files that do not have icon defined with html link tag.
If you want to define favicon with osclass theme then edit header.php file of your theme and add <link rel="shortcut icon" href="/favicon.ico" /> tag between <head> and </head> tags, it may be after closing </title> tag for example. And put ico file to your root folder.