Comfort for the dying can be so very difficult and to me, seems to depend on the belief and understanding of those who face demise. For the faithful, I do not consider that challenging their faith at the eleventh hour is at all relevant.
In life, we draw comfort and assurance from our achievements, from those we love, from our goals and ideals, our interests. The dying yet live- Such things still have meaning. We can focus on the achievements, the lessons that life has brought us, the future of those who will remain. For those who descry faith, we can assure them of the positive effect of their life cycle; of an end to suffering and of continuation in the memory, love and respect of those they leave behind. i believe it is important not to 'walk around' what is actually happening- This is readily apparent and causes awkwardness and discomfort, uncomfortable silences.
I come of a large, close knit family, many of whom have predeceased me. Perhaps my single biggest lesson is to leave my grief outside the room; bring my love and caring in.

There have been a lot of good suggestions, but I would ad, just ASK how you can help and let them tell you. Maybe they need actual help (rides to medical appointments) or reassurance or just company. I think if you just ask what you can do that would be most helpful and let them guide you.

I think just being there shows that you love them and is comforting in itself, with people that are terminal I try and only talk about death if and when they bring it up. (Although it can be tricky as it does come to mind more.) Talking about your shared experiences and honouring their life in that way with them is just as relevant, if not more so.
But they won't have to deal with their death as much as you will, so if there's anything you do want to discuss I'd:

• do a bit of work around what it is you want to discuss before you talk to them
• this will ensure that you only have to bring up the subject once and help you do it in a respectful manner
• remember it's healthy to think and even dream about the possibilities and probabilities of what will happen; it helps you deal with it when it does happen, just try not to dwell on the negatives unnecessarily, death is part of everyone's hand

Wishing you both the very best through this tricky time.

You are in a sad situation. If you are spending a lot of time with this person, don't you think you could ask them what they would like to talk about, and if they would prefer to talk about the future or the past? I am sure a lot of dying people would like to talk about what is happening, and what will happen, but they themselves are afraid of upsetting the loved ones they are leaving. We need to be much more open about death and our approach to it.

The people you love and love you don’t want you to suffer. Love one another, be good to them now while you can. Enjoy memories of how they improved your life and pay it forward.

The grim reaper will visit us all. Follow their lead in conversation topics. Pain relief is paramount. It has been found that the religious fear death more than atheists. Science is now studying how hallucinogenics
are relieving anxiety is the terminally ill. Who knew, as our government crushed any research until recently with soldiers suffering from PTSD. Just be supportive prior to the transition into the cosmos of energy that can never be destroyed but only changed into another form, according to physics.

I lost someone I loved and unfortunately had to watch him die in front of me. Its hard to do but when you are there with them its comforting for them. There are no right words to say just say what is in your heart.

I'd like to think I treat dying friends/family the same way as I treat the non dying. With respect and cherishing the time I am with them

Maybe you could broach it gently by asking if there is anything else she would like to talk about - it sounds as if you are panicking about something that is natural I don't know of anyone who has those words to hand & being there is enough. It is good to know that someone is there . Believe in yourself - You are enough she will talk if she wants to ,trust yourselves.

I personally do not fear death, I fear dying, as I do not want it to be painful. All we know about is our life and the way we lived it.

Remind them of all the good in their lives. The joy they brought people, the good deeds they did. There’s nothing to celebrate in death, it’s simply the end. Celebrate their life.

Though dying is tough for everyone, most true Atheists don't fear death. Why would you? It simply means that all the pain and suffering of dying is over. To fear the loss of consciousness is to fear going to sleep at night. The only real reason to fear death is if you have some sort of residual fear that you, or your loved one, might go to hell. However, grief is the feeling of loss and is perfectly natural. It is better felt than repressed. All my life I have known religious people who have grieved terribly in spite of their beliefs. The pain of a lost loved one transcends all belief.

Let them know you love them, and make them laugh as much as possible (as long as it
isn't super painful for them to do so).
Play them George Carlin clips off YouTube. Watch a lot of Monty Python.
Comfort, per se, cannot always be achieved, so in lieu of that, keep them amused.
And if they aren't on oxygen, smoke 'em out.

What I would want to know from the people that cared about me was that I made a difference to them. I would want to know that my life made an impact on the world and that people would remember me. I think that's about the best that any of us can hope for.

I think you are doing what you can by being with them. You can always ask if they want to talk about it or not.

My dad died last year he wasn't a believer. IMHO As long as you let them know that you love them and are there for them that is all you can do. Let them know the other people they love will be supported by you and they no longer need to worry. Dad wasn't all that old he however had been in terrible pain for as long as I can remember. Also if you aren't sure or comfortable with starting the conversation with them just ask if they are ok with you starting that conversation. If they say no at least they can tell you when they are ready since they know you want to talk. That is probably the best advice I could give. Hope that helps. Good luck