Start with the freezer. If the freezer is cold and the fresh-food side is warm, the problem is airflow: a fan, a frosted coil or a damper. If both sides are warm and the compressor is hot or silent, it is a start component or the sealed system, which needs a technician.
That one question separates most calls. Central Minnesota Appliance Repair diagnoses refrigerators across Minneapolis, St. Paul and the metro every day, and the freezer-versus-fridge test is the first thing we ask on the phone. It also tells you how urgent the situation is, because food safety depends on how warm the fresh-food side has become.