Good for you, it would be a pity to put paint on cabinets like yours. Wood grain and the proper stain, look so good.
Anyway, to answer your question, you have to sand and sand. Stain is a penetrating thing and the only way to properly remove it is to sand. if there is a polyurethane finish or top coat or varnish, you can use a stripper for this, but it won't remove the stain.
Get a good Makita orbital sander and a good Porter Cable detail sander and start in. Remember, use coarse paper at first and then work down to fine paper. Sand in the direction of the grain only. Do not stay in one spot too long.