Process of testing for food allergies? Do they interview you, give you a screening test, what happens?

See below. Your physician will listen your symptoms history, and may discuss family history of allergies, asthma, and/or eczema. Then testing through blood work or skin testing maybe performed.
That's right. 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.
History is Everythin. Food allergy testing should be done based on the history. If there is a concern for a food allergy, there should be a history of symptoms linked to specific foods, even if the link is tenuous. "shotgun" testing for food allergies can be misleading and produce false positive which can confuse the issue. I would recommend evaluation by a board certified allergist and discussing testing with them.