Let's start with setting up the News module to display a newsfeed. The News module is very touchy about what it will transform with it's defaults. So, far the best advice I can give you is to stick with feeds that are RSSv2.0. It also matters that you specifiy the correct URL for the feed. In your example, the URL you provide is not the URL to the feed, but to the host that provides the feed. Try using this URL: http://feeds.feedburner.com/DotnetnukePodcast?format=xml
Now, what you'll get is not probably everything you'ld expect, as the DNN News module will take a feed and do a bit of sanitizing and transform it into a 'DNN RSSv2.0' output. This means that if your input news feed has any special namespaces their tags will not be used in the final presentation. Only the bare bones tags from RSSv2.0 are presented, which really means it's more akin to RSSv0.91. You'll get 'title', 'link', 'pubDate', and 'description', but nothing more using the Default.xsl provided with the module.
Also, as you've noticed, the display of the feed relies on fetching the source using Ajax, and plays strangely with the Cache settings. I've had better luck, modifying the New module settings, and you'll be able to 'uncheck' the 'Use Ajax' option.
Start with this info to see if it helps somewhat. Then, we can tackle what that tutorial is discussing. I'll take some time to go over it. Lee usually has a good take on things, but some of the info is out of date, so I'll check on it.
One last bit, I'm using DNNv5.0.0, windows xp, IISv5.0, and the News module v.4.0.1. If you have a different setup, it helps to give your setup to better understand your environment.