The code for this is not a problem - what I don't know I'm sure I can find on the Arduino tutorial site, but I'm wondering if anyone knows where I would start on any sort of relay/dimmer system that could interface between the Arduino and the 120V 20A lighting circuits.
Thyristors and triacs are frequently used for AC light dimming.
This page: http://www.allaboutcircuits.com/vol_3/chpt_7/5.html seems pretty comprehensive.
I have heard of a light dimmer kit available (I believe it was an Elektor kit) that has an analogue input to control brightness which may prove to be suitable.
Mike