My AKC experience is old (over 10 years old) but you had to have paper work to do obedience trials. You might want to look for fun matches near you as a place to start.
For Schutzhund DVG does not require that the dog be registered or purebrerd but you have to have your scorebook to enter a trial. You are required to belong to a club to enter a trial. You are required to have a BH to do anything else and the dog must be 15 months old to try for a BH. Don't know what the requirements are for other organizations.