Some clarification on using a standalone WiFi router to connect iPads, iPhones, and Apple TV's together for presentations:
Using a standalone WiFi router with nothing more than its WiFi radio turned on will create a WiFi network which is all that is needed to use the above devices. This is not a theory; it's a tried and tested reality. The iPad will connect up to the Apple TV and the iPhone can control the iPad.
A standalone router will NOT give you access to the internet unless you connect one of its ports to another device or connection that supplies an internet connection. If you do this, make sure you use the routers "Wan" or "Internet" port. This will keep the routers DHCP service from interfering with an existing network.
When I say that you can just plug in the router and use its default settings, I'm trying to demonstrate how simple it is. In reality, if you use a router, you should activate its wifi security to keep others in the area from also connecting to your router. If you will be connecting the router to an existing network, you should also change the router's IP address so that it's on a different subnet than the existing network.
The Apple TV allows for a password (simple PIN). You might want to activate this if you have coworkers also using their iPads to keep them from accidentally (or intentionally) taking over the connection to the Apple TV (without a password, any iPad on the network can take over the connection).
Those of you doing presentations at trade shows might be tempted to just use the WiFi network that is usually provided at these shows. In my experience, these "public" networks are usually set to isolate the users from each other which would also stop the iPad, iPhone, and Apple TV from talking to each other.
I hope this adds some clarity to the idea of using a cheap WiFi router to create a network just for the purpose of connecting devices for a presentation.
--Dave