Look in the mirror. Tonsilloliths or so called stones in the tonsils are usually collections of food particles in the crypts (grooves) on the surface of the tonsil. You can see them in the mirror as small white round collections. They may represent bacterial colonies, food particles or small retention cysts. They often produce a foul odor to the breath and may be a minor indication for tonsil removal.
Easily. Eventually you hack one out. They're actually made primarily of keratin; as a pathologist I've seen enough under the microscope. Get a penlight and a mirror and half-unbend a paper clip. You'll get good at it. You probably won't hurt yourself. A water pick is even better. They do recur. If it's truly a nuisance, a otolaryngologist can laser-resurface your tonsils.