My understanding is that extending a wireless network would indeed work best with additional cable. The "simplest" means of extending a wireless network is to introduce additional routers that can "repeat" a wireless network to which they can join. I believe this is a problem because you need all the routers to play nicely with each other (OK if they are from the same manufacturer) and you are extending a weakened signal. For preference you should use a wired connection to link the routers. Probably the cheapest/easiest way to do this is using powerline ethernet kits that use the electrical wiring in your house. These are often quite cheap, do not require cabling to be installed, and seem to work surprisingly well. I'm using a kit in our 1950s house that still has the original wiring (aka deathtrap) and the speed is really good, certainly faster than 802.11n Wifi. One router should be the master and the others linked to it via the ethernet ports (link a normal ethernet port on the master to the WAN port the slave(s)). Each router should broadcast a wireless network of the same type with the same name and password, which should mean that devices will connect to the closest router to them.
I confess I've never actually tried to do this but I'm pretty sure that this is what I read a while ago.
Anyway, I hope that helps.