I think it's useful to start out by understanding that most of your audience is going to be some form of believer and will be to some degree challenged by atheism as a concept much less a real flesh and blood person. I'd start out by asking them to examine their attitudes and feelings about Thor or Odin or some other god they're highly unlikely to be devoted to, and explain that our disbelief in THEIR god is exactly the same to us. It is not a matter of hostility but of indifference. Challenge them to explain why they are Christian or Muslim or whatever they are, as opposed to something else; expose them to the concept that most people believe what they believe because their parents did and secondarily because it was reinforced by the society they happened to grow up in. These thought exercises will humanize us and challenge their assumptions.

Beyond that it's just a matter of conveying basic literacy about what an Atheist is and is not. We literally see no valid reason to believe in any gods; we don't claim to "know" there is "no god", the difference between generic ideas of god and specific ones, things like that. We don't hate god or believers, are not seeking moral license, don't necessarily have alternative lifestyles but are ordinary people next door for the most part, those of us who are activist or anti-theist don't object to people minding their own business and following their own beliefs but rather we object to believers imposing their beliefs or practices on others in the public sphere outside their private clubs.

I would also suggest that most of us have a thoroughly considered opinion, do not feel any more needy / lost / alone / afraid than anyone would at a human level, and so what we need are not religious bromides but human empathy. You can be present for people and comforting to them, without appealing to a god or a particular ideology. Unless your healthcare institution is a religiously sponsored one, it should be run neutrally, as a secular institution out of respect for all patients of any religion -- including no religion.

When I worked around people who were dying I would frequently sit with them and be grateful that I could comfort them in their final moments. And then I had a conversation with one who happened to be a different religion and she said I just pray for her because she's going to hell and I was horrified by that. When somebody is dying and they ask you to pray for them do you go ahead and do as they wish or do you pray to your own God? As an atheist I pray to whatever God they wish me to at the time that they are in need and it's no sweat off my back. But I was very dismayed to hear Christians talk so hatefully

I guess the most obvious thing is in a healthcare setting keep the random god botherers away. We do not wish to be prayed for, we do not wish to here about how our problems are part of "God's plan", etc. Also should someone wish to have their treatment withdrawn, respect their wishes, the whole sanctity of life thing doesn't wash with many atheists, they may be more interested in quality of life. The obvious follow on from that is a bridge too far for many but personally that is a pity.
Apart from that we are normal people though possibly more prone to ask questions about what is going on, pros and cons, and expect to get honest and complete answers.

Here are some questions that have been asked of me.

1. How can you be moral and not follow Jesus. Answer. I do the right thing withoiut the expectation of a reward in the afterlife or punishment.
2. You have to follow the bible which is the word of god. Answer. The same god who killed the innocent first born of Egypt. He just had to show himself to the Pharaoh. The same god that told the Israelites to kill of of the male children and elders and the older women and to only keep the young women of child bearing age and to wait three months until they took them as wives.
3. God hates homoxeuals and heathens. Answer If you truly believe in god, than god made them that way and if he made them that way then god gave them the free will to choose and you believethat, unless you think god made a mistake.
4. You should follow god or you will go to hell. Answer. Which god, which religion, Christian, which demonination, Judism, which sect. Muslim, which sect. Why so many and how all of them claim to be the true religion of god. Is god playing games with them. They all claim that god speaks to them.
   These are just some that I have had to answer and those are some of my answers.

Are you asking why we believe whatwewe believe? For me its simple. I was never taught to believe in god when I was a kid. I was never influenced one way or the other.