The PoE adapter consists of two components. The power injector, and the power splitter. The injector sends the DC voltage along the unused pair of the cat5 network cable. The splitter removes the power from the unused pair and feeds it to the device through a standard power connector. I used pairs 4/5 and 7/8 for my PoE adapter.

The injector: 4/5 and 7/8 are soldered to the tabs of the barrel power connector. It's the correct size for the linksys power brick.
The splitter has the male power connector wired to 4/5 and 7/8 in the same fashion. I made it an L style with some electrical tape to fit the tight confines of the enclosure.