How do you check up on an oral surgeon to find out about their qualifications?

Medical society. Call your local medical/dental society.
Ask about training. Inquire about the doctors residency program and any post residency fellowship training. Ask what professional organizations the doctor is active in and finally do they hold an active academic appointment at a teaching program or participate in frequent continuing education programs. Finally ask other patients how they feel about the doctor.
A number of ways. You can check with the state dental board to make sure their license is current. Aaoms.Org is the national society for oms's and their website will list member qualifications. Most oral surgeons have websites that will go into detail regarding their training. Make sure they are board-certified and a member of aaoms. This ensures that they have met the strict standards set up for oral surgeons.