I have never played a paper role-playing game, but I understand the basic concepts (I think), and I'm curious to find out how rolls/stats/xp/etc work, practically and statistically.

I know rulebooks are available for D&D, but they're expensive...and really, I want a basic and general understanding of the theory, not some complicated D20 rigamaroll. I also know there are online resources, but most of them seem to assume you already know how to play RPGs.

Can anyone tell me where I can find a resource on the basics?

Why bother? It easier to hop on a computer D&D game and play it with friends over the internet or ethernet. If you play a game like Everquest, you can focus on actually playing the game without worrying about the mechanics of it.

I have played pencil and paper D&D in my childhood. The problem is that those games cannot be finished in just one afternoon. Unless your friends are also D&D fanatics, they won't be interested in saving the game for later.

D&D rules are actually very simple. After you figure out how it works, you will feel like it's not worth knowing.

The usefulness of such rules can be interesting to some, and in the cases of computer games interesting to those that want to develop a story into a game model that people can play.

The SRD is available for free download on wizards site. It's a stripped down version of the d20 rules for use with the open gaming license.