What were summerian's beliefs in life?

Sumerians had no fixed group of Gods; each city had its own God who they built temples for. Often their rulers were also priests of the cities.

They believed that the earth was flat, capped by a round dome, the sky.

Sumerians were very devout and worshipped their city's Gods as well as the Gods of their families. It generally was believed that it was however a matter of chance and luck whether any prayers would be actually answered. Sumerians believed that after death you went as a ghost to a gloomy afterlife, regardless of how well or devout you had lived.