This question was answered in large part here:
http://talkabouthealth.com/what-can-an-esophageal-cancer-patient-expect-at-their-first-meeting-with-the-gastroenterologist. In general, the best test for suspected esophageal cancer is upper endoscopy (EGD). This will allow visualization of the esophagus and identification cancer if present. After cancer is diagnosed, a CT scan of the chest, abdomen, and pelvis as well as PET imaging are typically performed. Early stage cancers may be managed by the gastroenterologist, while more advanced cancers are managed by the chest or cancer surgeon and medical and radiation oncologists, who administer chemotherapy and radiation therapy.