Many blogs and news websites these days have an icon as shown in figure here. These icons get you started with subscribing to those websites. To learn how subscribing works, you can start with clicking on the image, which will subscribe you to this website.
After you click on this icon, a webpage will appear which shows how the feed from this website will look on your RSS feed reader. Feed reader is nothing but software which decodes the XML formatted RSS feeds and presents to you in a human readable format.
The same page also gives you the option of selecting to subscribe to the feed using one of the feed readers among Google, Yahoo, Bloglines etc. If you have an account on Google or yahoo already, you can use that account to subscribe to the feeds, else you will need to sign up with one of these websites which requires filling up a simple form. Once subscribed you may then log in to the reader site you chose to read the feeds from your favourite websites.
Apart from the above mentioned method, there are other methods of subscribing to blogs and websites as well. You may simply log in to your feed reader and chose to add the URL of your website to get feeds from it. However, not all websites allow their feeds. Some may not be configured to allow feeds while some may block them. You will get an error message in such a case.