To
overcome anxiety, one must understand the logic of why the brain is feeling threatened, it sends messages to the body saying its under threat. New pathways need to be created to overcome the old programming. So for example, if you panic over a fear of flying, you must start flying and let the brain realise that its all okay, and reprogram the thoughts.
However, the fear of dying can't really be practiced. Some buddhists meditate in a morgue as it is the closest we can get to dying.