The most expedient method is surgical removal of the stones. This method is required for calcium oxalate stones. Struvite stones can sometimes be dissolved using a specific prescription diet, though this often takes 1-2 months.
Other methods of resolving stones are less commonly employed. Lithotripsy is a procedure that uses either shockwaves or a laser to break down stones after which they may be removed by an endoscope or allowed to pass on their own. My own kitty was treated with shockwave lithotripsy while I was in veterinary school to break up his single bladder stone, allowing him to pass the smaller pieces. This method can be successful, but the equipment is usually only found at universities or specialty hospitals and is not used by most general practitioners.