The certificate could be easily enabled through the Magento Admin area -> System -> Configuration -> Web. There you can define the insecure (non-SSL) and secure (SSL) URLs:
In the Base URL fields you should enter the unsecure (regular) web site URL and the web site URL for the SSL connections. You can leave the other values unchanged, as they will be set automatically by the script after you enter the Base URL. Basically the other fields define the URLs of the main Magento store page and the URLs of the skin, media and JavaScript folders. The drop-down menus allow you to enable and disable the SSL support for the web site's frontend and backend.
Bear in mind that the SSL connection over HTTPS is slower than the HTTP, thus secured connection should be applied only to the pages that contain and process sensitive information. Also, it is recommended to run the admin interface through an SSL. In this way you will increase the security of the script's backend.