The steps to change joomla faviconis quite simple. First you need to need create the favicon and then upload to the right folder where the icon resides.
First step! Create your joomla website favicon.
Create your image in a perfect square dimension for example 100px width times 100px height, then generate the favicon usinghttp://www.favicongenerator.com/
Another website that you could use to generate favicon ishttp://www.favicon.cc/ You could create the favicon using the website tools easily.
I just created one nice favicon using the site, to check it out Click Here .
Once you have created your favicon, upload the favicon to template folder of your joomla website.
If you're newbie, not sure which template you are using. To find out your default template, access your joomla admin >> then click Extension >> then Click Template Manager.
Your website template is marked with the yellow little star as shown below.
Then access your website folder, you could access by using your cpanel or viafile transfer protocal software (ftp software)
Go to the folder of the joomla template that you're using for example my folder is at yoo_enterprise
Then, just delete the old one and upload your new favicon icon. That's all, done.
Please remember to use the same file name for your favicon icon as the previous favicon icon.
If the old favicon file name is "favicon.ico" , keep the new one as "favicon.ico" .