How to breakdown kidney stones?

Surgery. The mainstay of treatment for kidney stones is surgery. If the stone is very small, medications may be used to help pass the stone spontaneously. However, for larger stones, surgery is the only option. Surgery includes endoscopic framgentation of the stones with various forms of therapy such as laser, electohydrohydraulic lithotripsy, or eswl (the bathtub with water).
See list. Calcium stones (80-90% of stones) can be managed with shockwave lithotripsy, laser lithotripsy or percutaneous lithotomy. Uric acid stones can sometimes be dissolved by increasing urine ph to 7 or greater. (bicarbonate (sodium bicarbonate) or potassium citrate can accomplish this). Calcium stones can not be dissolved chemically.
Kidney stone. Kidney stones up to 5mm in size will predictably pass on their own. Just drink plenty of water so you produce a lot of urine, dilate those ureters and allow the stone to pass. It may hurt while it's on its way out, but it'll pass. Bigger stones will likely get stuck and will cause tremendous pain and will have to be removed by lithotripsy or cystoscopy.