What do we learn happens to the people when they die? How do Bernard and Lenina respond to this ?

In Brave New World, people are cremated after they die and then forgotten.
As Bernard and Lenina fly around in their helicopter, they see the four chimneys of the Slough Crematorium. It is lit up so helicopters don't crash into to it. It is described as "majestic" and also as a "landmark."
Bernard and Lenina have no fear of death or the crematorium. Bernard notes with approval that the crematorium is able to capture and recycle 98 percent of the phosphorus from a person's body. He says:

“Fine to think we can go on being socially useful even after we’re dead. Making plants grow.”

Lenina is similarly practical, but having been conditioned to feel that she, as a beta, is superior to the lower castes, she is surprised that their bodies produce as much phosphorus as upper caste bodies.
Bernard and Lenina's casual and pragmatic approach to death as a natural process is a result of their conditioning. We learn that:

Every tot spends two mornings a week in a Hospital for the Dying. All the best toys are kept there, and they get chocolate cream on death days. They learn to take dying as a matter of course.

This is a sharp contrast to John the Savage, who grieves deeply when his mother dies and doesn't understand why children are all around the hospital.