In images folder which is inside the template, replace favicon.ico with yours.
Make sure you have cleared your Joomla and browser cache before refreshing your site. The steps for doing this are listed below.
|Joomla 2.5||Admin -> Site -> Maintenance -> Clear Cache|
|Joomla 3.x||Admin -> System -> Clear Cache|
|Firefox||Admin -> System -> Clear Cache|
|Chrome||Admin -> Chrome -> Clear Browsing Data|
|Safari||Admin -> Develop -> Empty Caches|
|Opera||Admin -> Opera -> Delete Private Data|
|IE||Admin -> Settings -> Safety -> Delete Browsing History|