I have been searching the internet for ages and did not find a very concise answer to that question. You can find software on the market that will help you create the XML file for your RSS service, such as FeedForAll ( a very suitable name).
Now to come back to the topic, has it become old school? Tweeter will offer you preaty much the same thing, except that most of people write lots of nonsense as well on their “tweets”. But if you decided to use tweeter just to post links to your blog page for each new article , than it can serve as RSS. And it will be found by other directories that compile blogs and other articles.
But RSS feed does give a bit of a professional touch to a blog page and it also helps other websites to find your blog pages. So the answer is in my opinion, not yet an old school, but not the only way to provide a feed from your website.