RSS (Really Simple Syndication) is a simple way to get news from your favorite sources. Rather than visiting all your favorite websites to check for new information, you "subscribe" so that news is delivered to you as it is published.
The most common option for reading RSS feeds is to use a RSS news reader or aggregator. One popular, free one is Bloglines; no downloads are needed but you must register. Sage is an extension for the Mozilla Firefox browser that you can download and use to subscribe to RSS feeds. Find many more options through Yahoo.
The method for subscribing to a feed can vary somewhat depending on the particular reader you use. Usually you simply click on the orange RSS or XML button, copy the feed's URL from the displayed page, and then paste it into the reader.