Use a spudger to disconnect the two antenna cables from the communications board. Apple used a small dab of glue on these connections, which may make removing the antenna connections harder.
Working from the edge opposite the battery connectors, insert a spudger between the battery and the plastic frame and pry up on the battery. It is attached to the casing with an adhesive, but should slowly come free.
Leave the battery resting slightly out of its housing, but be sure not to put too much pressure on the battery wires as the solder joints break easily.
Slide a spudger beneath the logic board on the side opposite the battery connector and pry up slightly. Don't lift up too far, because there are still four attached connectors on the bottom of the logic board.
In a similar manner, slide a spudger beneath the logic board where the camera was. Again, don't lift up too far yet as there are still four attached connectors on the bottom of the logic board.
Continue to separate the two boards. The silver metal shielding may not immediately separate. If necessary, work around the edge of the board to separate the metal shielding.
If you are replacing the communications board, you need to desolder it from the battery. The battery replacement guide can help you remove the battery.