I just did this with my home network so here you go.
First things first: use the new wireless router as the primary router, and the wired one you have as the secondary router, because you want the wireless router to be running the DHCP server.
Only the router actually hooked up to the internet connection should be running the DHCP server, so go into your second router's setup and disable the DHCP server.
Change the second router's IP to something other than the IP for the first router. Most routers default to 192.168.0.1, so I suggest changing to to something like 192.168.0.25.
When you're connecting the routers together, you must connect them from one LAN port to another LAN port. You can not use the WAN port on the second router.
This means that if you are using two 4-port routers, you'll be left with 6 ports to use.
(actually, now that I think about it, it might not matter which router is primary and secondary, but whatever)