Answer:
Thalssemia is diagnosed by performing blood tests. Complete blood counts will tell you the amount of hemoglobin, red blood cells, white blood cells, etc. present in the blood, and people with the disease will have considerably lower levels of healthy red blood cells and hemoglobin. They may even have smaller red blood cells, which would be an indication as well. Secondly, special hemoglobin tests can be done to determine if a patient's hemoglobin has normal alpha and beta globin protein chains.
Usually, a child with severe thalssemia will be diagnosed because they will have severe anemia early on, in which case, blood iron level tests can be done to cross out anemia due to iron deficiency. In more mild cases, anemia is also the determinant of a diagnosis, but happens later on in life and would usually come about after a routine blood test indicates anemia.
Lastly, if an individual has a family history of thalssemia, they may have genetic tests done to determine if they are carriers for the disease. This should happen before they have children. If they are carriers, they may have prenatal tests done on the placental fluid of any children they conceive to determine if the fetus has the disease.