It is pretty easy. The main issue will be the initial setup as your old box will have retained your last config. The instructions below might not be 100% accurate for your setup, but they should give you the gist of what you have to do.
1. Disconnect your computer from your new box
2. COnnect it to your old box on one of its LAN connections (the box should still be configured to provide DHCP addresses)
3. Go into its configuration screen (probably 192.168.0.1 or something like that)
4. Find the appropriate menu and DISABLE DHCP (probably 'Network Settings' on the left side of the configuration page and 'Setup' on the top side; then UNCHECK the 'Enable DHCP Server'
5. Reboot the old box.
6. Reconnect your computer to the new box.
7. Connect one of the LAN ports of your old box to one of the LAN ports of the new one.

Wi-Fi clients should see a straight Ethernet network accross both boxes. The LAN ports and the Wi-Fi ports are as if connected to the same physical switch. The fact that only your new box allocates IP addresses will ensure that your applications will understand to which box to send packets going to the Internet.

Hope this was enough details. Do not hesitate to ask if they did not work.

See Mojo's signature