Death as we know it can be Cardiac or Neurologic. Cradiac death fortunately remains something most physicians are comfortable pronouncing. Brain death on the other hand is a little more detailed.
Cardiac Death: When the heart stops beating and there is no return of spontaneous circulation after CPR. Look for the flat line on the EKG. Accompanied by fixed dilated pupils and lack of sponateous respirations. Now you have most ingredients to safely make a death pronouncement.
Brain Death or Death by Neurologic Criteria : In order to diagnose brain death, you have to demonstrate the absence of both Cerebral and Brainstem activity. First there has to be a definite cause of irreversible brain injury eg. intracerbral hemorrhage. Begin the exam at the eye. Check for pupillary light response, corneal reflex and dolls eye. Now hold the eyes open and perform cold calorics in both ears. Move down to the mouth, check a cough and gag response. Now move on to the body and check response to painful stimuli. If all the above responses are negative, we are ready to do the apnea test. Get a baseline blood gas. Unhook the patient from the ventilator and observe patient for ten minutes. Now repeat a blood gas. The PCO2 should have increased due to the lack of breathing. Now you should be able to pronounce the patient dead.
The above description only serves as a primer. If you are still interested, follow the link below for a more detailed , well illustrated description of brain death criteria. You can also take the test at the end of the activity , if you want to get certified. I suggest you get the certification. The entire activity is free.