- Make note of the first router IP address range and DHCP pool. Check what wireless channel it is using.
- Make sure DHCP pool is not "everything", like 192.168.1.100 to 192.168.1.200 is fine for example... Router#1 should be at 192.168.1.1 in this example (yours may be different)
- Log into second router from computer via wired connection. Turn off it's DHCP. Set it's address to 192.168.1.2, gateway 192.168.1.1 (first router), same netmask.
- Change #2 router's wireless channel to something different than first. Use channels 1,6 or 11. Change the SSID as well.
- These steps make each AP different for now, to be able to test if everything works ok.
- Power cycle #2 router, then plug cable from LAN port to LAN port of #1 router. Do not use WAN port, you are using #2 router as a switch/Wireless device only.
- Plug PC back into #2, and note that your IP address is from DHCP pool on #1 router - that means the network is working.
- Connect to second router wireless, to verify it works.
After all this works, you can experiment with the wireless being the same SSID and channel, to allow roaming. Some routers do it well, others argue with each other. So, it may end up that you have to keep separate channels and connection profiles for each router access...
All IP addresses are examples. Yours may be similar but different, like 192.168.0.1 or 192.168.2.1
WDS is also an option like others say. However, your wireless bandwidth may be less than regular wireless. How it works may depend on the router and what Internet bandwidth you have (WDS will slow down a high speed internet (20mbps+) connection)