Can I set up an RSS feed on my site or do I need to do it through an existing blogging site? How does it work?
You can absolutely set up an RSS feed on your site. How you go about it will usually depend on what kind of framework your site is using. Just as your local computer has an operating system, like Windows, webpages often aren't just HTML pages but are quickly and easily created by a certain kind of platform, or "framework" that writes the code for you. I do web-design myself, and I am particularly fond of using Drupal. I know for a fact that Drupal-created websites have RSS modules, but I have no idea what you're using.
If you're designing a website from scratch, writing your own HTML code (wow, I'm getting a visual image of a housewife in the 1900's trying to do ironing with heavy, antiquated industrial machinery!), you'd probably want to use PHP code to do it... or pay a PHP coder to write code for that purpose for you. Many job sites exist, particularly sites that allow you to offer programming jobs to PHP coders in need of them. Project4Hire, for example, is a site where you can post a job and have professional PHP programmers submit lower and lower bids for your project. The result is that you end up paying about the lowest price the market will bear for your project, by people who can do it.
Were it me, I'd use Dapper - a free online tool - to scrape my page if there was no other way, and put it into a Sprout that I could embed on my pages somewhere... or anywhere else, for that matter. But ideally, I'd want to look into using a framework like Drupal to build my site, rather than do it all by hand. If you already are using some kind of a framework, you might want to check your documentation or online site for it to see if it has RSS capability, or an add-on module that does. Most online blog forums offer RSS feeds to their users.
In addition to Dapper, other RSS scrapers exist out there. Metacentric, for example, offers a for-pay scraping service that is free to try.
Recently, illegitimate RSS scraping is starting to be used by unscrupulous people on the 'net who use AdSense to generate revenue on their own sites, just as HubPages does for its users. These people scrape the content off of other peoples' news sites and blogs and then post that content on their own "scraper site" pages that are made specifically to generate AdSense revenue, with lots of ads and banners. The pages are specifically designed to bring users and show them lots of ads, in the hopes of generating revenue through ad-clicking.
Still, at the end of the day it's comforting to know that even if you're designing your site by hand, you can still scrape your page with Dapper into an RSS file, and then post that feed as a Sprout. So, there's at least always a way, no matter what.