The first caveat is that you must eat wheat (gluten) for the whole month before you are tested to get the most accurate evaluation. Blood tests are performed that check your antibodies, including the most sensitive test (meaning it will miss the fewest cases, but may have some false positives) -- the anti-tTG (anti-tissue transglutaminase antibody) test.
The doctor must also test your IgA levels (immunoglobulin A) because if you are not making adequate IgA, you could test negative for celiac disease even though you have it. Additional blood tests include anti-endomysial antibody (EMA-IgA) and anti-deaminated gliadin peptide (DGP – IgA and IgG).
Ultimately, the diagnosis will need to be confirmed not only with a blood test, but with a small bowel biopsy which is done through endoscopy. The biopsy will look directly at the lining of the gut and determine what level of damage exists.
Alternatively, you can choose to follow a strict gluten-free diet, and if your symptoms resolve, it is likely you have celiac disease (or at least gluten-intolerance). This is obviously less specific and accurate, but is certainly a good starting place.