I've lost numerous beloved dogs and cats, and I can't for the life of me, remember how I got thru the loss of most of them. Maybe that's a good thing tho, since I remember them all now with smiles and fond memories, and not the tragedy of the end. Some went fast and others lingered and I waited longer than I should have to step in and help with one of them - something that I will NEVER do again.
I really don't know how anyone can be of any real help to another, other than to say "I'm sorry". We all have to - and do - find a way to get thru it on our own and in our own time. It's a very lonely and personal road that we each have to walk down, in our own way.