Welcome Hagerty members, this is a motor sport I have been involved in my whole life. I wanted to introduce and provide some resources for the community. Here in Michigan we have three large promoters that sanction the races from county fairs to one-off race events. This year's schedule is up in the air, but here are some links to promoter's schedules to find a race in your area, or rule books that guide you toward building your own racer.
USA Demolition Derby: http://www.usademoderby.com/
Unique Motor Sports: https://unique-motor-sports.com/
TNT Demolition Derby: https://tntdemoderby.com/
Barriers to entry are relatively low, from the entry level "Stock class" for front-wheel drive car, to the competitive "Modified, big-car" class I compete in.
Modified Class, 1975 Oldsmobile Cutlass