Everything I know is here:
http://aiaonline.org/activities/robotics
Interesting quotes from the tournament guide:
No entry fee to participate in the AIA Robotics State Championship.
and
All students eligible for membership on a FIRST Robotics team will be eligible for the AIA Robotics State Championship.
I'm still looking for how the community teams, Caution and BinaryBots get in; the AIA seems to have done "The Right Thing" (YEAH!) by inviting them.