How can archaeologists study prehistoric peoples who left behind no written records describing their lives?

The correct answer would be artifacts. Archaeologists use artifacts and features to study how people lived before. They want to know what these people’s daily lives were like, how they were ruled, how they interrelated with each other, and what they understood and appreciated.  Sometimes, artifacts and features provide the only evidences about an ancient community or civilization because prehistoric civilizations did not leave behind written records, so we cannot read about them.