Basically all you have to do is compiling a valid RSS file (kind of XML) and offer your visitors the possibility to subscribe to this feed using their RSS reader.
Since you probably do not want to write XML by hand, there are tools for creating a RSS feed file:
1. If you use a CMS to manage your website the functionalitly to create the feed file are probably already built in?
2. Install some ready-to-use RSS managment tool server side, which allows you to create, maintain and deliver feeds directly on your server.
3. There are some online tools that allow the enter feed information and the entries. The tool then creates a valid RSS file which you can save locally and upload to your server.
4. Use some Mac/Win software to edit the feeds on your PC. Most programs allow direct FTP upload to your server. This is the way I do it...
Creating the feed is easy, promoting it is not. How can you tell people about your feed:
* If you have newsletter subscribers, send them a mail about your new RSS feed along with some explanation about RSS and its use, esp. free RSS readers they can download.
* Add the well-known orange [XML] or [RSS] icon to your website and link it to your feed file.
* Adding a "Whats this?" link underneath the icon leading to a page describing the concept of RSS and the use of RSS readers always helps to get new users into using RSS.
* Add a :: type="application/rss+xml" :: to the <a href> tag which points to the RSS file. This helps some RSS readers to identify feeds by themselves.
* Add something like <link rel="alternate" type="application/rss+xml" href="myfeed.rss" title="RSS feed for my website"> to the HEAD-section of your page. This can help too...
* Submit your feed to RSS search engines.
I can not post any links here but some google searches for relevant terms should point you into the right direction. For questions you can PM me...