Suppose I make my own HTML code and want to put it into a website. Now don't think I'm dumb, because I'm still learning the basics of web design (though I know a lot of JavaScript). If I want to use my OWN computer as the server for that website, let's just say a “Hello World” page, how would that be done exactly? How would I incorporate my .html files into a Web Page that can be accessed with my computer being the server?

You could just have a set of html files and a browser would render this for you straight from the hard drive. It's only when you start introducing dynamic pages and specifying URL's like http:// rather than a file location that the you can't use your file system and then you need a web server. In which case you would then need to install one on your computer.

Just like drmcw said. The best web server program is probablly Apache, but if you're learning it doesn't matter that much.

For html, javascript, and css files, you don't need to have a server of any kind - just open the file in firefox or another internet browser. If you want to include php, mysql, or other server-side things, then you have to install some software. I use a package called XAMPP that combines an installation of apache, php, mysql, and some other things. Keep in mind though that this server will only work on your local network.