The following pictures give you three different views of a typical set of steering coils:
The steering coils are simply copper windings (see How Electromagnets Work for details on coils). These coils are able to create magnetic fields inside the tube, and the electron beam responds to the fields. One set of coils creates a magnetic field that moves the electron beam vertically, while another set moves the beam horizontally. By controlling the voltages in the coils, you can position the electron beam at any point on the screen.