The objective of the teardown is to break down the carb into small enough pieces that they can be inspected and cleaned. When the teardown is completed there are a bunch of really small pieces (stuff in the egg carton picture above) and some miscellaneous larger pieces (stuff on the white towel picture above) and the three main carb pieces; Air Horn (upper left), Body (upper right) and Base (lower center) of this picture.
As mentioned above, do not remove and tear down the butterfly valves. The screws that hold the plates to the shaft will be destroyed during disassembly and they are not easy to find. Also, keep as much of the linkage attached as possible. This helps upon reassembly. If the carb needs work in these areas, it might be best to send it off to the professionals.
When progressing through the teardown, everything should be kept neatly organized and together. Taking lots of notes and pictures is appropriate. Some time will pass between teardown, cleaning and reassembly and it is very easy to forget what goes where.