One bite at a time. So, that is what must be done with the picture. It is broken up into small pieces by a scanning process, and send one line at a time, with each line containing hundreds of bits of the picture. This is called the video signal. In early cameras, various forms of special tubes were used for this process.
Modern cameras use solid state devices that do essentially the same thing.
Color images are sent in the same way, except that there must be a signal for each of the primary colors used. Yes, our old friend radio strikes again. The radio waves that carry television pictures to you are the exact same radio waves that carry the news to you in your car. The only difference is the type of information they are carrying. In conventional broadcast radio, the radio waves carry a sound, or audio signal, while in television they carry the video signal.