Construction Details
The Express' case was very tightly put together, so I didn't try to crack it, instead relying on pictures from the FCC ID documents for the view of the main board shown in Figure 3.
Figure 3: AirPort Express Main Board
(click image for larger view)
The main board contains the Broadcom processor - which I suspect is the BCM4702 Wireless Network Processor (although it could be the newer, more powerful BCM4704 - and Broadcom AirForce radio. There are actually three boards packed into the Express' little case, the other two hold the audio circuitry and AC power supply. If you want to see more pictures of the Express' innards, check out this site, but be warned that the pictures aren't lit very well.