I doubt that anyone can give you this much detailed explanation here at EE. There is A LOT of background information that you need to understand, and if you do not know anything about RSS and XML, you will need to get that understanding before you can know what questions you need to ask!
RSS is a specialized subset of XML. Begin your learning process by reading up on RSS here. You will want to read it thoroughly and follow the links.
http://cyber.law.harvard.edu/rss/rss.htmlTo learn about XML, start the process here. There are entire books devoted to the subject (I have three), but Tizag has a good intro, as do others.
http://www.google.com/#hl=en&q=xml+tutorialTo get the article information into an RSS feed, you would write a script that executes a MySQL query. The query will get the basics about the articles - title, date, author, etc. The script will format this information from the query results set into the XML, using the subset of XML that is RSS. Then you will write the XML file into a predictable place on your server. This can be done in the background, or scheduled via a "cron" job, or if it is a very active feed, it could be done on every page load.
To present the RSS feed to your clients, just put a link to the XML file on your web site, same as any link.
Once you have an understanding of some of the background and you have specific questions, please post back here and I will be glad to help you get it working. A sample RSS feed file is attached. They all look alike.
Look at this page, on the right sidebar and click the link that says "News via RSS"
http://www.ntcicfunds.com/Best regards, ~Ray