How is a TV controlled by a computer?

The traditional meaning of TV is that of an RF receiver (the "tuner") and a display unit. A Traditional TV set is a piece of analog technology; there is no digital component or computer interface. You cannot control one of these types of TV from your computer.

However, modern TV sets are specialized computers themselves, implementing some of the image control and user interface technology digitally. Many modern TV sets are already able to handle digital inputs both from an aerial (terrestrial digital TV) and from other sources, such as an HDMI input to connect a high-resolution DVD player or similar equipment.

Those TV sets might have a physical or logical interface to your computer. For example, the TV set itself might provide a small web server which you can use to connect your PC to the TV much like you visit any other web site. In case of a TV, you might be able to alter settings and view status information, for example.

More recent TV development often includes some form of "connectivity." Some units can access the internet through wireless or wired LAN connections and display YouTube videos, for example. Others can display and play content from local DLNA servers, playing your digital music, photo or video collection from your home network.

There is no commonly accepted standard way of implementing "connected" TV sets, and all vendors try to gain a competitive advantage by supporting a few standard technologies (e.g. the HTTP and DLNA protocols) plus something of their own invention. Therefore, there is no single correct yet generic answer to this question, as the availability of PC-to-TV connectivity and its features is subject to the exact choice of TV model.