Once the SSL you have purchased is installed, simply upload files and pages as you normally would.
If your site was http://www.hostgator.com, to use the SSL you would add a "s" to the http. The link would now become https://www.hostgator.com and load securely.
But my site still says http?
Your home page should always be http. You only want to use https for your online forms and places where protected information needs to be sent over the internet. So, for those pages, just use https in the link name.
(For example: on the home page, link to "https://domain.com/contact.html".)
You can alternatively create .htaccess rewrite rules to force your home page to use https. (Relative links, like "contact.html" will thus use https; however, absolute links like "http://domain.com/contact.html" will force http instead of https.) Here is a site offering you the codes:
Force https for your home page.