The RT-N56U device of Asus is a so called router, not a modem.
The router can optional be configured to work as an access point only.
The modem (Modulator-Demodulator) is connected to the incoming line of your ISP, either a DSL line (telephone line) or TV antenna cable. The modem picks the "hidden" Internet signal from the telepnone line of antenna cable and turns it into a standard TCP/IP network signal. Modems are often provided by the ISP.
The network signal out of the modem can be brought directly to a single computer to give it Internet access.
Todays households do have more than one computer or device that require internet, to distribute the single Internet connection out of the modem to multiple devices, you use a router. The router has a buildin network switch with multiple network ports to connect multiple devices.
Most routers these days also provide wireless access, and have a buildin wireless access point. So, with most routers like the RT-N56U you can use wired devices and wireless devices.
To extend the wireless coverage, you can hookup another wireless access point to the router. Most routers like the RT-N56U can also be configured to be an access point only.
You also mention gateway, a gateway is a device to connect one type of network to another type, with different protocols. In normal households that is not applicable.
Reading your question I believe that you want to setup the RT-N56U as router and the RT-N66U as wireless access point.
Am I correct? Otherwise rephrase your question with above knowledge in mind.
Main question is how you want to connect the RT-56U and RT-N66U together, wired or wireless?
The RT-N56U router I assume is working and shall be untouched.
In the RT-N66U look at:
Advanced Settings>Administration>Operation Mode
There are 3 options, if you click either (without Apply), you get some helpfull explanation about each mode purpose and setup.
Access Point mode requires a wired connection between the RT-N56U and RT-N66U.
In Advanced Settings>Wireless>Bridge, you find information about setup of a wireless connection between the RT-N56U and RT-N66U, so called WDS, Wireless Distribution System. WDS with standard firmware is not recommended because it only supports unsafe wireless encryption.