I was toying with getting a 2nd broadband connection in my home to ensure that I always have a connection, so I gave this some thought.
At its simplest, you have router A with internal address of 192.168.0.1 and router B with address of 192.168.0.2. Router A is the DHCP server, with DHCP service switched off on router B - assuming that you are using DHCP.
Your clients are all on the same subnet as the 2 routers, but in normal operation their default gateway is 192.168.0.1, being the better connection. In the event that router A or its upstream connection fails, you would switch A off, enable DHCP on router B and run a DHCP release / renew (IPCONFIG /release, IPCONFIG /renew in the Windows world.
Your clients are now connecting to router B for their internet connection.
Of course you can use fixed IP addresses, in which case you just have to change the default gateway manually on each client.
If you want to use both connections, you can use non-overlapping DHCP scopes, still within the same subnet, or use fixed IP addresses to achieve the same effect, such that some devices use router A and some use router B, using one of the above mechanisms to cater for failure.
Using DHCP in this way is a bit hit & miss as to which device connects to which router, but for me I would use fixed IP addresses for all PCs, and DHCP for phones & tablets.
SD