They are mainly two types. Skin prick test and blood test for Specific IgE against allergen (thing causing allergy).
Skin Prick Test Specific IgE by ImmunoCAP / RAST
They both have similar degree of accuracy. SPT, gives you results in 15 min but can not be done if the child has taken any antihistamines in last 48-72 hours or has no area of skin unaffected by eczema. Blood results can take 7-10 days to come back.
In some cases, the test may be negative, but the child may still be allergic or the test may be positive but the child may be able to tolerate that particular food. This is called sensitisation (it’s complicated). Best test for allergy is Oral food challenge, where you give the suspected food (under medical supervision) and see what happens !!