I then am little confused as to where to connect the power and ground of the arduino. Do i connect the ground to the emitter, and also to the ground of the NES? And then connect the power to the collector, and also to the 9V from the NES?
You don't connect ground to anything on the transistor, or the power to anything on the transistor. To use the transistor as a switch in its simplest form you need to saturate the transistor when its on, and have it at cutoff when its off. Basically, data pin through a resistor to the base like you said, and each contact of the "switch" would be an emitter or collector.
The thing you need to find out is what current you need through the base to get into saturation, which depends on your specific transistor, and not to exceed the Arduino's max output current.
Although, that said, transistors can't switch AC voltages. You said the power supply is 9V AC, so that might be an issue. That's probably why a relay was mentioned.