It depends on how much dose a person receives. The dose at which 50% of the population dies within 60 days without treatment is about 500 rem acute whole body dose. At this dose (called hemopoeitic syndrome), a person's bone marrow is sharply ablated and there is serious risk of infections. There is usally some hemorrhaging as well. However, with modern medical treatments (such as transfusions, clean rooms, etc.) the risk of death is reduced, though the victim can continue to have complications for months. At higher doses, the GI tract is affected, which complicates matters even more. At doses high enough to affect the central nervous system (around 1000 remwhole body), the only real treatments are palliative. At really high doses (2500 rem+), the vicitm is usually unconscious within a few hours and dies in several days.
Please note that these doses are hundreds of times the annual maximum dose allowed by regulatory agencies, and thousands of times the natural background radiation. This means the only real way to get this kind of dose is accidentally.