The first thing to know is that what you do depends on one fact: whether the death was expected. If the person was on hospice or under a doctor's care for a terminal illness, you do not call 911. If the death was sudden and nobody was expecting it, you do.
That one distinction changes who you call, who comes to the house, and how fast any of it happens. This page walks through both, plus the calmer things that are true either way: you are usually not on a clock, you choose who takes the body, and a lot of what feels urgent can wait an hour while you sit with the person. Steps vary by state, and where they do, this says so.