I want to know how to have the source articles appear on the page without having a completely different page for each article.
My concern is that if I have 100 articles in 100 individual .html files and I need to update a link in the header or sidebar, I then have to edit all 100 pages. Can I have 1 article list page that, when an article is selected, the contents will populate in a master template page.
I'm pretty good at finding these answers on Google, but I'm not sure exactly what to search for. So I'm not necessarily looking for a tutorial, but rather some terms/phrases that I can search on that will help me find what I'm looking for.
It sounds like you're looking for a CMS. These will allow you to manage such content without having to worry about managing individual pages on a website. Most CMS's have the notion of "templating" where you'll design a template for a specific use case (i.e. articles, home page, categories, etc) and this will be reused on each page type.
As for recommendations, the best CMS around for PHP is Concrete5 and the best for ASP.NET is Umbraco