I see that you live just outside of Cinci.
South Ohio is AMA District 11 for racing. Are you interested in motocross or hare scramble racing?
The District 11 2003 schedule is here:
http://www.district11ama.com/2003_Schedule.htm
and more District 11 information here:
http://www.district11ama.com/
Basically... to get started racing you will need an AMA card ($39 for a year)
www.ama-cycle.org will help or you can buy one at your first race. I also think D-11 requires a District card (can also be purchased at the first race). Then you will be all set. Pick a race on the schedule and go for it. Normal gate fees to get into a race are from $5-10 a person and race fees are usually $20-25.
What type of bike will Austin be racing? In District 11, there is a 4-8 50cc oil injected class for the beginners (mostly PWs, XRs, JRs) and a 4-6 50cc class (mostly Cobras, KTMs, Polinis, LEMs).
I would recommend trying to practice at a track ahead of time before Austin's first race just to get him familiar with the track. If you are racing motocross, on race day he will get a practice (usually 2-5 laps) then normally two motos (two 2-5 lap races). Of course make sure to have all the proper safety gear (helmet, boots, gloves, goggles, long sleeves, pants, chest protector) before he gets on the track.