Making a routed client, which is what the ddwrt tutorial was about, is the simplest way to do this. The down side is that it doesn't truly bridge to any LAN devices that may be connected to the other router. This is not important for many users, in fact it may not even be desired-- for example if the other router belongs to a neighbor (connecting with their permission of course). Basically you are going to replace the typical ethernet connection to a modem with a wifi connection to an existing access point. Your LAN works internally the same as if you had your own connection. It only use the wifi link to access the Internet.
Start at default configuration.
Set your router's LAN address to 192.168.2.1. You have said the other router is 192.168.1.1 and you need to be in a completely separate range for this to work. If you know the other router is not using 192.168.1.X you can skip this step.
Disconnect and reconnect the ethernet cable so your PC picks up the 192.168.2.X address, put 192.168.2.1 in your browser and log into your OpenWrt router again.
Go to Network -- Wireless and click Add. Set the new interface as a Client. Enter the SSID and security settings to match the other router. Select wan as the network.
Go to Network -- Interfaces -- edit wan -- Physical Settings and uncheck Bridge. The wifi client must be the only device in wan.
Go to the main status page and confirm you have an IPv4 wan connection. You should now be connected to the Internet.
(Last edited by mk24 on 9 Mar 2017, 16:37)