We buried my father almost two years ago. He was not a None, but he was a Jew. He said his prayers intermittently, kept most of the commandments most of the time, was a somewhat reluctant regular at the synagogue, and didn't really believe in anything supernatural. So I found out what people do at the end of life if they don't believe in an afterlife.

My father strove to make the most of every single moment of life he had left from the moment he was diagnosed until the moment he fell dead. Earthly life is precious to people who don't believe in heaven. Once next year became irrelevant, he stopped thinking about next year and turned his attention to the next day. 

When it was over, he was buried with the traditional Jewish burial ritual. The whole thing took about fifteen minutes, because the balance of Jewish opinion on death is that nobody knows what happens afterwards and all one can do is hope for the best and leave it to God, if He exists.