How does the hypothalamus communicate with the anterior pituitary?
Through blood vessels.
The functional connection between the hypothalamus and the anterior lobe of the pituitary is vascular. The network of blood vessels between the hypothalamus and the anterior pituitary is called the hypothalamic-pituitary portal system / circulation.
The superior hypophyseal artery drains through en bunch of capillaries into long portal vessels. These long portal vessels descend to the anterior lobe of the pituitary (adenohypophysis; see image).
The function of this circulation is to deliver hormones to the anterior lobe of the pituitary. These hormones are produced by small neurons in the hypothalamus.