I may say something like, " I know this is the hardest thing in the world, but just know that it gets easier with time".

Sending love and hugs...my thoughts are with you...here for you.

Yes, this is a time when letting the grieving person know they are in your thoughts is acceptable. Depending on my relationship with the person suffering the loss, I might offer some tangible help, if there's something they can use, whether it be to take a walk and talk about how they feel, or some help with meals or cleaning, packing up their loved one's belongings, etc.,

Of course, in my line of work (conducting funerals is part of what I do) I make myself avaiaable to conduct the service or offer resources for conducting their own funeral service, memorial or ash scattering.

I say I am sorry it happened and that I'll be remembering them.

I usually share my condolences.

My condolences as to your loss, nothing about death is fair to anyone, I hope the memories you have of the deceased bring you peace and comfort for the rest of your days.

It varies depending on my relationship with the bereaved, but there are several things a non-religious person can say. I'm very sorry is the best, though.

Sometimes I ask if they have looked in the last place they saw them. That's what I do when I lose something.

It's never received well, I've found.