The Missile Computer is used to control Missile Tubes and allow them to fire. They must be linked to the arrays in the same fashion as the Cannon Computers are linked to Cannon Barrels. Use C to select the controller, and V to add a link to the Array. You can also skip the need for manually linking by placing the Computer first and then adding the arrays afterwards, as they will automatically link.
Once the Tubes have been linked to the Computer, you can press T to link the Missile Array to your hotbar.