As my 16 year old Daughter ( often quite wise for her age I think) said to me during her last few days of life, "Dad, grieve for who I was, love me for being who I was, enjoy the memory of me and the times we shared BUT don't mourn my passing instead celebrate that I was once alive and enjoyed being alive. As the Klingons in Star Trek say, 'the body is just something the real person needs to travel around in, once it is no longer useful, like any vehicle we discard it, ' mine has become too damage to be repaired and that is just how things go."
As for the "In a better place" comment, in my opinion, the only "better place" is the place where you are right now and what YOU have made of it, it IS all up to you.

I struggle with this. I usually say that she will never be truly gone as long as she's in your memories, celebrate and treasure the good times, no lomger suffering, etc. Nothing anyone can say truly helps. It's going to take as long as it has to in order for the pain to lessen.

I am saddened by your sadness. I also send a note telling them how it is not about how much they miss the departed, but how lucky they are to have them to miss. Sorry seems like an accepted, but lazy word. Using the same word I say for being late or forgetting something in regards to their loss of a loved one feels empty to me. Still, it is nice to hear it in a moment of grief

They remain forever in your memory.

Great suggestions. Thanks everyone!

I try to be realistic and say "they are no longer suffering", if that fits or "you really made their life worth living" or "I'm a better person for having known them". I don't elude to a hereafter at all.

I have noticed that here I America, people don't like to say,"he died" They say " we lost him" or " he passed." For the longest time, I had to bite my lips and not blurt out"you didn't lose him. He is right there. He's dead." I got over that compulsion . Now I say " I am so sorry for your grief"

My thoughts are with you at this difficult time. I am sorry for your loss.

Is there anything I can do to help? - this will vary or not be appropriate depending on how well you know the person.

I'm sorry.

I don't believe they are 'in a better place', so I would never use that phrase. No longer in pain is something I might say after a long illness.

sorry for your loss

My father died from cancer. So, being not alive, not in pain, is a better place. I think using that term is appropriate in that instance.

And my inner Nihilist hangs with Freep's inner nihilist, so sometimes I think that.

My inner nihilist says being dead is being in a better place. But he's an ass.

That's a tough one. Our culture and laws are so very derived from religious ideals, as well as human moral values that it is tough to say something under those circumstances. Condolences is the safest I've found, but then it's not about us. It's about the person that's grieving for the one they've lost. While I never say I'll pray for them, I might play along on their behave. Crossing the rainbow bridge, or you're in my thoughts, or as you said, they're in a better place, etc....
Of course the opposite of that is when someone says to you, You're in my prayers, I'll pray for you (and/or them) or They're in heaven now. That can be uncomfortable at times too, especially if you know the person well and that they've been devoutly religious all their lives.