How are food allergies tested?

Oral challenge. History trumps skin & blood testing for food allergy. With a history of a reaction like hives, difficulty swallowing, throat tickle, vomiting, asthma or anaphylaxis minutes to hours after eating a food negative skin & blood tests are insufficient to rule-out allergy. A positive test is usually convincing. Mostly we do unblinded challenges in the office reserving double-blind for ambiguous cases.
Skin or blood tests. Food allergies can be tested by either skin testing or by blood testing. However, the gold standard to prove a food allergy is the double blind placebo controlled food challenge.
Skin test. Food allergies can be diagnosed by history and skin testing. Often if the test are equivocal, then an oral challenge is done with the food. The food can be given in small amounts either in a "blinded" form (ground up in capsules) or in a pure form, and the individual observed for a length of time.
True allergy-IgEonly. Either a skin test or a blood test for IgE to the food in relation to your clinical history is the best way to diagnose food allergy. Blood tests that use IgG4 or a combination of these (IgG4 plus IgE) are not meaningful. If your health insurance tells you that they will not approve a test, be suspicious. It may not be a valid test. Check out http://acaai.org/locate-an-allergist.