Fault-tolerance/redundancy for home wi-fi?

I'm looking for a way to broadcast my home wi-fi network in multiple parts of the house in order to increase signal range. Rather than set up some sort of signal relay system, I'd like to use multiple routers to broadcast the same wireless network from locations near opposite ends of the area.

The ideal goal: I can walk through the house with an internet-capable device and its connection will remain intact as I move away from one router and toward another, without me having to connect to a different network. If standing within range of both, failure by one device should not impact my connection due to the other supplying the same network.

What I'm working with: AT&T U-Verse DSL, two modem-routers.

Step 2: ???
Step 3: Broader signal

Can anyone help? Thanks!