Well, the basic idea behind the game is that you have one Game Master, and several players, usually three to five. The Game Master is sort of a combination of movie director and football referee. He provides the scenario the players are going to be facing, controls the opponents they’ll be fighting, and judges the difficulty and outcome of any actions the players attempt. RPGs differ from most other games in that the intent is co-operative, not competitive. Although the GM is in control of the enemies the players are fighting, his goal isn’t to defeat the players, but to provide a challenging and rewarding game experience for them.
The pieces of paper are mostly character sheets, which are the same sort of collection of statistics, skills, and equipment as you’d find in a video game. You also usually have a lot of blanks paper for keeping notes, drawing maps, etc.
The dice are used for random number generation. In D&D, you have 6 different kinds of dice, with four, six, eight, ten, twelve, and twenty sides. You use these to generate your character’s statistics, and later to determine the degree of success at any given action.
The books are, indeed, rulebooks. They tell you how to make characters, which can be a fairly complex process, depending on which RPG you’re playing (D&D tends towards the complex side of the spectrum). They describe how the game engine works. They also provide specs for weapons, spells, and monsters. As to how binding they are on the GM, it really depends on the gaming group, and to a lesser extent, the game. Some groups tend towards a lot of rules lawyering, memorizing all the aracana of the game and insisting it be followed minutely. Others are more interested in what makes a good story, and consider the rules to be a not-entirely-necessary nuisance.
Another common feature of RPGs is the use of miniatures, which make it easier to keep track of where everyone is in a battle, and allow for more sophisticated combat strategies. They can use printed maps, like the one seen in the link, sophisticated terrain, or a simple wet erase mat with a printed grid, and some markers.
The interesting thing about the above is that none of them are strictly necessary for an RPG. A lot of people don’t bother with miniatures, and just sketch out the combat on a pad of graph paper. There are several diceless systems out there. Some gamers use purely homebrewed systems, and don’t have any rulebooks. Some games don’t even use the GM/Player set up, encouraging everyone at the table to engage in creating the story. The only standard is probably the character sheet, but even then, it can range from a multi-page stat sheet, to a 3x5 card with a short bio and some personality traits.
If you’d like to see (well, hear, anyway) how a typical D&D session goes, the guys who make the guys from Penny Arcade and PvP got together with one of the designers of the latest version of D&D and put out a series of podcasts of themeselves playing the game. They’re fairly amusing, and pitched at a very introductory level.
The thing about PnP (Pen and Paper) role playing is that it varies wildly by group. It’s far more social than even an MMO, and the conventions of the group are more important than the rulebooks. Some groups spend most of their time fighting monsters and taking their stuff (referred to by some as “roll” playing), others will be focused almost purely on character development and interaction; most seek a balance between the two.
