The way to do this is by using a wireless bridge connected to your router. A bridge basically receives the wireless signal and outputs it to a wired Ethernet port. You would then take the output of the bridge an plug it into the lan port of your router. You may be able to use the wan port but not certain in your case. Try the lan port first. Since you want a home network you will use the DHCP server in the router to assign ip addresses to your devices. In this case you want the to use the router almost in an access point mode in not in router mode. Having never done what you want you may need to try both wan and lan ports to see how it goes.
Regarding the bridge itself Id suggest you use a repeater in bridge mode. Basically a...