adding wireless router to wired network

1. When researching this topic, I saw that the wireless router’s lan port should be connected to the wired router’s (which is the gateway providing the internet) lan port. I don’t see why. Doesn’t the internet signal go from the modem into a router’s wan port, there to be distributed out through the lan ports? So the wireless modem’s wan port should be connected to the gateway’s lan port!
2. All the posts said the 2nd router’s DHCP must be turned off. That didn’t work. No IP got assigned to the wireless computer. When I left DHCP on, it assigned an IP address, and everything worked. The server is running the 1st DHCP, not the wired gateway. Any ideas why this is so, please?