How do we find a good doctor that can address my mom's back pain and knee arthritis?

References from family and friends are always a great place to start. You can also do some research online. You might also want to consider a gerontologist. A doctor specialzing in treating the elderly has knowledge of many of the conditions and ailments associated with aging including arthritis and back pain.

You can use the AgingCare Directory to find a gerontologist in your area. Here's the link:
www.agingcare.com/Find-Senior-Care