My house is just a little too big to get good wireless access in all corners. I'd like to add a second access point. I can do this, but I have to manually configure this second AP to have the same keys, etc. Is there any way I can get this second access point to get its configuration from the primary one? What would this be called and what sort of hardware or firmware do I need to do this?
What you look for is one of Wireless Distribution System or Universal Wireless Repeater.
Not all routers suport this though.
It is not uncommon to look for models that support and install DD-WRT or any other of the open-source firmware.
There are however a few routers that support WDS. You should be able to find a good list in the Wikipedia entry: WDS on WikiPedia
You might also like to read about Universal Wireless Repeater here
I agree with getting a range extender/repeater. If possible, try to buy one that is the same brand as your router. We seem to have had issues with DLink repeaters working with Linksys routers, but if we stick with Linksys it works fine.
Or....seems like I have recommended this alot lately. If you have another router, try running DDWRT on it in repeater mode.
Larger companies use this kind of configuration when they want to have a common configuration. It can be thought of essentially a central access point with multiple 'antennas' on the network. However, this is comparatively very expensive.
For a home setup, if you have two APs as the same model, you could write a script to run on a host on the network that automatically pulls the config via the network from the first AP, tweaks a few values (IP address, name, etc.) and pushes it to the second device.
However, unless you change parameters often, it's probably easiest just to configure the second device manually.
Since it is non industrial application and your range is not a huge one, I suggest to use a range extender instead of new AP. It has a higher transmitting and reception power so you can get more range than standard wifi.