What is a common medicine for reducing kidney stones and pain?

No..., but...: Kidney stones usually cause no pain as long as not moving. If moving and causing local tissue irritation and urine flow blockage, its related pain can be highly erratic in its onset, degree, duration, and interval. As to reducing stone, i assumed you meant reducing recurrence; if so, maintaining daily urine output > 250cc and decreasing oral consumption of salt, red meat, ; dairy products by >50%.