What is the charcoal snake method and how does it work?
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.