I know 800x600 screens occupy a shrinking part of Web surfers, but I want to accommodate them by offering an alternate style sheet where my site pages don't break when someone from this smaller group visits. Yes, there are examples of how to do this on the Web, but I have one more requirement and don't know how to code it. Not only do my pages break on 800x600, they also break if the browser widow is sized smaller on a 1024x768 screen. (I'm studying css that will dynamically respond to this but I'm not there yet.)
Do I just need an appropriate if/or statement to deliver different style sheets? Is there even a JS that detects browser window changes?
Sounds to me like you're looking for CSS Media Queries.
There's a very good article about it over at ALA: A List Apart: Articles: Responsive Web Design
That's an excellent suggestion. I have read other A List Apart articles and they're always top notch.