I've read in places about using something called the charcoal snake method for slow smoking in a kettle bbq. What is it and how does it even work?
Here's an example picture.
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This is the method I use to smoke meat in my Weber! The basics are exactly what you see in the photo, with one more step. Start about a dozen (or in a 22.5" grill like that one, maybe 18-24) briquettes in your charcoal starter (you have one of those right? if not, go get one, they're awesome). When the coals in your starter are glowing, carefully place them with tongs at one end of the snake.
This is a super low maintenance way to smoke meat. It keeps a small number of coals lit far enough away from your meat that you have indirect heat similar to an oven, and the smoke is metered because only a limited amount of wood catches. The coals at one end slowly light the remaining coals and you can cook this way for hours. The circle in your photo will probably burn for 4-6 hours. If you add more coals as you cook, you can keep this method going for very long cooks (I've done a brisket doing this cooking for something like 14-18 hours). You'll want to rotate your meat as you cook to keep it directly opposite (or maybe a bit closer to the lit end so you don't have to rotate as often).
This blog post for SA's blog has a bunch more information and some pictures of one of my cooks using this method.
I assume you light one end. The charcoal then burns along the path creating very low heat and smoke. Seems like it would work, but my worry would be the quality of the smoke. For a detailed analysis of techniques, click here: http://www.chefsteps.com/activities/barbecue-techniques
The goal is to maximize the cool spot in the grill, so you can cook larger items slowly. I'm not aware of there being any magic to it, other than being a differently shaped fire for indirect cooking.
Unlike your typical two-level fire, you don't need a hot area to sear over, so it's pushed as far to the edge as possible to create a larger cool zone. I've personally never used this tecnhnique. I've typically started my coals in a chimney, then dumped them around the side of the kettle. It's possible that the coals may stay cooler and burn longer than using a chimney to make sure they've caught well.