1) In the standard Blender file, use SHIFT+A in the 3D View to create an Empty Mesh. This will be invisible in a render.
2) Select the Camera in the Outliner by clicking on it.
3) Holding down the SHIFT key, select the Empty in the Outliner so that both Camera and Empty are selected.
4) Click inside the 3D View.
5) Type ‘CTRL T’. This will pull up the constraint menu. Click on the middle option ‘Track to constraint’
It matters that the Camera is selected first and the Empty is selected second. In this order, wherever you move the cube, the Camera will turn to track it. In the opposite order, the empty will track the camera. To see what the camera sees, click ‘0’ on the number pad. If you do not have a number pad, remember to enable number pad emulation in User preferences under Input. I’ve saved this file as my default so that I can easily control the camera direction in my renders.