Setting up my Airport Extreme properly with multiple routers on a home network

Question

I have a 4 bedroom house that over the years has had router after router added in different rooms. I recently bought an airport extreme and an airport express as I am getting sick of not being able to network everything as well as to have one strong wifi.
So I have set up the Extreme in my office and the express at the far end of the house and it's doing wonders in boosting the wireless signal. This is what I am trying to solve:
How do I make all the wired routers apart of my wired and wireless network? The router/modem that was installed by Verizon obviously should stay. I read in another forum that NAT should be turned on and all other routers shouldn't but would be bridged. I logged into the admin settings for the router and couldn't find any place to change this.
As you can tell, I am no IT. So I am sure this may all be confusing. My ultimate goal is to have a shared hard drive on my airport extreme and shared printer on my express and all computers on the same network, communicating to each other. Currently I have 3 routers + airport extreme and express all connected.
Hope someone has the patients to help me out.
Thanks.

Answer 1

Good diagram!
In that case you definitely want the D-Link to act as a switch, and its manual describes how to do it:
(page 10)
Connect to Another Router
If you are connecting the D-Link router to another router to use as a wireless access point and/or switch, you will have to do the following before connecting the router to your network:
Disable UPnPTM
Disable DHCP
Change the LAN IP address to an available address on your network. The LAN ports on the router cannot accept a DHCP address from your other router.
To connect to another router, please follow the steps below:
Plug the power into the router. Connect one of your computers to the router (LAN port) using an Ethernet cable. Make sure your IP address on the computer is 192.168.0.xxx (where xxx is between 2 and 254). Please see the Networking Basics section for more information. If you need to change the settings, write down your existing settings before making any changes. In most cases, your computer should be set to receive an IP address automatically in which case you will not have to do anything to your computer.
Open a web browser and enter http://192.168.0.1 and press Enter. When the login window appears, set the user name to Admin and leave the password box empty. Click Log In to continue.
Click on Advanced and then click Advanced Network. Uncheck the Enable UPnP checkbox. Click Save Settings to continue.
Click Setup and then click Network Settings. Uncheck the Enable DHCP Server server checkbox. Click Save Settings to continue.
Under Router Settings, enter an available IP address and the subnet mask of your network. Click Save Settings to save your settings. Use this new IP address to access the configuration utility of the router in the future. Close the browser and change your computer’s IP settings back to the original values as in Step 1.
Disconnect the Ethernet cable from the router and reconnect your computer to your network.
Connect an Ethernet cable in one of the LAN ports of the router and connect it to your other router. Do not plug anything into the Internet port of the D-Link router.
You may now use the other 3 LAN ports to connect other Ethernet devices and computers. To configure your wireless network, open a web browser and enter the IP address you assigned to the router. Refer to the Configuration and Wireless Security sections for more information on setting up your wireless network.
While reading the above bear in mind the Verizon box is your router. Don't overlook any of the details in these instructions - read all of it and understand its implications. If I were doing it the first thing I'd want to know is how to reset the DIR-601 to factory defaults since I'd be sure to muck it up about a dozen times before getting it right.
It sounds as though your Express is configured correctly. It is providing a wireless access point for your wired network, the one created by your Verizon router.
The optimal configuration for this design is to configure the Express to create a network using the exact same wireless network name and password as the one created by your Verizon router, otherwise you will have two wireless networks. Leave its "channel" on "automatic" so it won't conflict with whatever the Verizon is using.
It will look a little like this:
I'm assuming some of your devices still need 802.11g so the "radio mode" will most likely need to be b/g compatible.
When everything is up and running, experiment with the wireless transmitter power for the Verizon router as well as the Express. It's best to use the least amount that will work for you, so as not to create needless wireless interference for everyone else. This also minimizes the possibility of people piggybacking on - or trying to hack into - your wireless network.
As far as getting your Windows computer to see your external HD, I haven't a clue. I'm sure it's possible but I'm not a Windows expert.