How do I treat arthritis without taking medicine?

Depends on the type. That depends on the specific type of arthritis. Gout does well with low purine diet. Exercise is good for many types of degenerative arthritis. Auto-immune types of arthritis need medications though.
Many ways. There are many ways to treat arthritis without medicine. These include physical therapy, therapeutic heat and cold, aquatherapy, bracing, orthotics as well as various supplements that may help. Talk to your doctor if you have one.
It depends. Is it rheumatoid or osteo-arthritis? In the treatment of osteoarthritis (degenerative joint disease), frequently physical therapy is used to treat the pain and functional limitations associated with arthritis. Electrical stimulation, ultrasound, other physical modalites (ice, heat), range-of-motion and strengthening exercises can all have positive effects on the arthritis.