What does an allergist or an immunologist do to diagnose food allergies?

A logical approach. The allergist takes a detailed history & then performs a physical examination. Rather than screening food allergy tests more likely to reveal false positives the allergist prefers, when possible, to perform tests relevant to your history. They may be skin or blood tests, sometimes both. If the diagnosis is uncertain oral challenges are performed in a safe setting with appropriate safeguards.
Allergy testing. After a complete history and physical, an allergist can do testing for the offending foods. This is typically done by skin testing, which allows you to evaluate for many foods, quickly, accurately, and inexpensively. An oral challenge is sometimes done to confirm an individual is able to tolerate the food.
History. The diagnosis of food allergy is extremely dependent upon the patients history. When you see an allergists, you should expect a detailed history and physical exam to be done. If your history is suggestive of food allergy then skin testing and / or blood testing will be done to confirm to refute the clinical history. If there is still concerns or questions about the diagnosis, the an oral challenge.