Occasionally when a device breaks, the defect is obvious. Whether it is a blown fuse or a defective capacitor, generally the easy to see stuff is easy to fix. When a problem is more subtle, or when doing some more advanced tasks like adding functionality to a device, greater knowledge about a circuit board is required. While there might be details hidden in lower levels of PCB, often just knowing the mounted components and layout of the outside layers can be enough to create a rough schematic of a device. [Throbscottle] has put together an excellent guide for procedurally breaking down a photo of a board and turning it in to something useful. The guide utilizes some open source image processing software such as the GIMP, Inkscape, and Dia, all of which are widely available. Keep in mind this reverse engineering can be a time consuming process, but will almost definitely reward those patient enough to work through it.
[Thanks to everyone who sent this in!]