Physical examination and laboratory tests would be used to investigate a patient with thyroid swelling. Laboratory tests would include thyroid hormones (T4 and T3), TSH, and thyroid autoantibodies to check for hyperthyroidism, hypothyroidism, or an autoimmune cause. Radiological tests such as radioactive iodine uptake quantification and thyroid scintiscanning could further identify areas of abnormal thyroid activity that may indicate conditions like Graves' disease, multinodular goiter, or thyroid cancer. Together these examinations would help arrive at a diagnosis for the patient's thyroid condition.