The other day, while helping an agency build accessibility into a Silverlight project, the designer asked where he could see an example of a screen reader in action. This is a reasonable question, since the vast majority of web developers and designers have never observed someone using a screen reader. And simply trying to use one yourself is likely to lead to frustration and little real empathy for everyday users of screen readers. You can't really test accessibility by having sighted people conduct usability tests using a screen reader.
I recommended that my designer friend check out the classic YUI video showing Victor Tsaran using a screen reader. Be sure to watch starting around the 25:00 minute mark where Victor speeds things up to what is normal speed for him.
The other advice I often give people wanting to understand the user experience of someone using a screen reader, is imagine that users are browsing your site using the Lynx web browser. This advice works best if you actually have used Lynx a bit, so you understand what it's like to navigate in a linear, link-oriented fashion. If you don't use Lynx, or if the page heavily uses AJAX, you can get an idea by simply dumping the list of the links on the page in linear order, along with alt tags for any images.