The most common cause of hypoparathyroidism is surgical hypoparathyroidism. This occurs in the setting of surgery of the thyroid gland, parathyroid glands, or other neck surgeries. In patients who have undergone a parathyroidectomy for HYPERparathyroidism, the sudden loss of PTH can lead to "the hungry bone syndrome"--a condition which is explained by the rapid absorption of calcium by bone once the PTH stimulus causing calcium efflux from bone has been removed. Fortunately most cases of surgical hypoparathyroidism are transient.
The most common cause of hypoparathyroidism other than surgical causes is autoimmune-mediated hypoparathyroidism. This can be caused either due to immune-mediated destruction of the parathyroid glands or due to activating antibodies against the calcium-sensing receptor on parathyroid chief cells. Autoimmune hypoparathyroidism may be an isolated disorder or may be part of a larger autoimmune dysfunction termed polyglandular autoimmune syndrome type I, in which hypoparathyroidism occurs in conjunction with chronic mucocutaneous candidiasis and adrenal insufficiency.
Abnormal parathyroid development--which can be seen in complex syndromes such as DiGeorge's synrome--can also logically result in low circulating PTH levels.
More rare causes of hypoparathyroidism include radiation-induced hypoparathyroidism and infiltrative diseases of the hypoparathyroid glands (e.g., Wilson's disease, sarcoidosis, hemochromatosis, or metastatic cancers).
Finally, there are various genetic mutations that can result in hypocalcemia, which are most relevant to pediatric nephrologists. For example, autosomal dominant hypoparathyroidism is caused by gain-of-function mutations in the calcium-sensing receptor gene: you can think of this as akin to being on sensipar all the time.