I don't think that anyone forgets their first death because one of the true gifts of nursing is that we are with people and families at the moment of their passing. Experiencing death is one of those things that you just know that your first "time" will be a raw, unpracticed affair and then over time, repetition will make it a little easier, but never mundane, because this is someone's passing from this life. To this day, some deaths will hit me hard and surprise me in the intensity of feelings. All deaths confront us with our own limited existence.
Nurses have a different role in different types of death. In the individual whose death is anticipated, our role is helping the family to be there and with the family to the extent that we are able and they want to be. Model respect toward the dying person and model loving touch, because some family's won't feel they have permission to touch their loved one. Some people benefit from having clergy, hospice nurses, other significant people, present; others don't want it. I like to keep an eyeball on significant others. Are they overwhelmed by too many or too few people? Do they need permission to walk out and get a cup of coffee or food? Some people feel that dying people will choose a moment like this to die, because they want to die alone. I cannot speak to that, but it is surely in the possible realm of human behavior. All of us develop our patter over time. Take your cue from nurses who are comfortable with death care and notice what they do. Try to find some one you can talk about the experience with. Try to have an expectation for yourself that you are a student of "death care", and watch how other nurses do it. Seek support and information from other nurses on how they like to handle it and what hospital routines are for post-mortem care.
To me, the other death scenario is the code and we get really caught up in this technology explosion, and have less concern for the family _at the particular moment in time_. Increasingly, some hospitals are allowing families to remain present for codes. I've not experienced this, but find it a worthwhile idea. I think you have to pick your family well and have a staff member there exclusively for the family (clergy or a nurse). Treatment after declaration should continue to model respect and loving touch and usual post-mortem care.
Give yourself permission to admit that you don't know it all in this area. None of us do. Have someone you can vent to over this when it does happen. Remain open to the intense spirituality and power of the moment.