They both appear to mean "to stand up".
立つ has much more range. It's used to mean "stand," as in a prolonged action; standing in one place. 立ち上がる is just the action of standing up. If you google image, it's easy to see the difference. 立ち上がる has another meaning of, basically, "rising from the ashes", like here: 破産の憂き目から立ち上がる.
立つ on the other hand has a huge range of meanings, just hop over to your favorite dictionary. If it's any good, it should make things clear.