If "deal" is related to actual tasks: Notify MD, family, coroner, provide post mortem care, arrange for spiritual care if indicated. If "deal" is related to emotions, then it depends on where they died: home, LTAC, SNF, ICU, Med Surg, OR, ER - were they a full code v/s DNR, if it was expected, or was it after an attempt at resuscitation? Depending on the circumstances surrounding the death, your response may vary. At then end of the day, you should allow yourself to time to process and if you need to go for a walk and/or take a lunch break. If you have the ability to debrief with your team that helps, or speak to someone from Spiritual Care; other support may come from Employee Assistance Programs that may be offered as part of your work place benefits. Even though I am not religious, I would say a little prayer of loving kindness to honor the life that was lived.
After giving post-mortem care and consoling the family (if they are present to come in and see the patient), take a monment to care for yourself. You did the best you could. You just lost a patient. If that doesn't bother you, no matter how ill they were, it may be time to ask yourself if you are "burning out". If you are in hospice care, you know this is going to happen, so it is a bit different. In the ER and ICU we always sent the nurse whose patient had just died off the floor for a few minutees so s/he could take a breath and refocus. If you practice a particular faith/spiritual path, feel free to say a silent prayer. If you share a faith with the patient and the family and they ask if you would pray with them, that's OK also. If you don't share a faith, offer to pray quietly while they recite their own tradition's prayers aloud at the bedside. I always taught my nursing students to tell the family it was a privilee to care for their loved one - because it is. If a particular deeath gets to you, go speak to employee assistance, social work, or the hospital chaplain's office. In some hospitals here in NY, a psychiatric NP will be available to staff as well. Perhaps where you work also? When my husband died, his ICU nurse read a lovely meditation at his bedside (while other staff were also present) called The Pause. You can google this. It is standard in many hospitals to be read at the time of a patient's death as a sign of respect for the passing of a human life and comfort fro friends and family present.
Normally I perform the post mortem care, coordinate with the funeral home or take them to the morgue. Done.