Back in August of 2013, Bart helped me figure out how to wrest control from the Verizon Actiontec FiOS router and let my Airport Extreme control my network. It was non-obvious, so he drew a diagram that I turned into a full tutorial per his instructions. The basic idea is to disable WiFi on the Verizon router, and have it simply pass out IP addresses using DHCP and send traffic straight through to the Airport Extreme. We also set the DMZ on the Verizon router to a static IP and passed that right to the Airport. The purpose of that step was to eliminate the requirement to do port forwarding on both routers if I ever needed to access something inside the network.
All of this worked great, I was able to pretty much ignore the Verizon router for the last three years.