It’s a little harder with static sites to get an RSS feed because you can end up duplicating content if you are not ready to add another tool to generate your site or you are programming a bit (and maybe the language is different from the ones you use currently.)
As @Simone noted, RSS is a simple format and easy to write. But if you just write an RSS feed on top of what you are doing right now, you will obviously duplicate some or all of the content on the site, which is not ideal.
So, I would advise that you need to use your content and convert it to an RSS feed - or vice versa.
When I created a static content site with an RSS feed, the way I did it was to start with an RSS feed. Then I wrote code that would use the RSS feed and create my HTML articles. In my case, I used XSLT to convert RSS to a series of HTML files, but you could use whatever technology you want.
Then, when I wanted to add an article to my static site, I would edit the RSS feed to add a new article with a new date, etc. (and there are tools for different platforms for manually creating RSS feeds like this.) Then I ran my code that “burned” my HTML articles, so I always get static articles and RSS feeds in accordance with each other, and only one "source", a copy of the content.
There are also tools for various platforms that can automate or semi-automate the creation of an RSS feed from many things on disk, which is a way to approach the problem from a different direction.
Therefore, I answer that if you are not ready to add a language or tool other than CSS, HTML and Javascript to your repertoire, there is no satisfactory way to add an RSS feed to a static site. If you just added it as a static file created manually, then you need to update your content in two places if you are editing an article, for example.
You can also learn a lot about how the modern crop of tools for creating static RSS-based sites is Jekyll , or its more reasonable derivative of Octopress , for example, complete an assignment.