It Revolves on This: The Hub and The Spokes

At almost 600 pages, The Burning Wheel rulebook is a monstrously huge tome. The good news is that you don't have to bother with a large chunk of it in order to get a game going. In fact, it's discouraged if you want to have a successful game.

The core of the game is called "The Hub and the Spokes", and is the foundation that the rest of the game builds upon. These first 75 pages are really all you need to get a game off the ground. Seriously. Some of my earliest failed attempts were simply due to trying to engage too much of the system at once.

For your first few sessions, possibly even your first campaign, stick to the rules in this section. Focus on writing interesting beliefs, mastering intents and tasks, and creating dynamic failure consequences and you should see the Artha begin to flow.

Once you have that down, you can consider what you want to add to your game. The other sub-systems crank up the drama, but also come with a considerable amount of rules crunch that will interfere with learning the basics.

Finally, you can get those rules for free from BWHQ here.