1) In the configuration.php file where it says "Live Site URL" for Joomla make sure you enter an https:// url so all the content/modules can be called securely.
2) In the index.php you may want to change any Google Font calls that are set as http://googlefonts
... to //googlefonts so they can be called securely or non securely
Those are the only things that would affect an SSL certificate. If you have issues beyond this please post a URL that illustrates the issue so I can take a look at what the certificate is blocking. Also note that SSL certs often require you to specify with or without www.