After a good 3 hours of fighting with my Airport Extreme and Airport Express wireless network, I finally had an epiphany: ignore all the Apple documentation, help wizards, etc. and just guess. Luckily, I guessed right...and now I'm passing it on.
PROBLEM: How do you connect and use an Airport Extreme and three Airport Expresses in the following configuration:
--- Cat6 wired --- Airport Express <--> wireless clients
Airport --- Cat6 wired --- Airport Express <--> wireless clients
Extreme
--- Cat6 wired --- Airport Express <--> wireless clients
In English (a language not spoken in any wireless setup manual), this problem is "hey, I've got my house wired with Ethernet and I want to be able to set up a bunch of wireless access points so I can get wireless everywhere in the house, stream AirTunes, etc. How do I do that?"
SOLUTION: As soon as you realize that Apple's setup manual terminology is designed to confuse, this is really, really easy.
Step 1: Factory default every device (basically, hold down the reset while plugging it in).
Step 2: Configure the Airport Extreme by choosing "create a new network": the key settings are (1) pick a network name, pick a channel (NOT automatic), pick a type of security (I did WPA/WPA2), pick a password. All the other defaults are fine.
Step 3: Configure the first Airport Express: (1) choose "Create a new network" (trust me, illogical, but correct); (2) use the SAME network name, channel, security and password as in step 2; (3) under the "Internet" tab, choose "bridge mode." That should be it.
Step 4: configure your other Airport Expresses the same way as step 3.
BONUS! If you want to stream AirTunes somewhere without Ethernet (in other words, join your network wirelessly), follow this set of steps: (1) factory default the device; (2) choose "join a network" (same network name, channel, security and password); (3) under the "Internet" tab, choose "bridge mode."
Good luck!