Voyager's camera used a vidicon tube, which is sort of a vacuum tube precursor to a CCD.
I don't 100% understand the principle, but the basic idea is that the image is captured on a photoconductive surface, thus converting it to a pattern of electrical charge; an electron beam is raster-scanned across the photoconductor producing a varying voltage out of the system, which can be amplified and converted to a digital data stream. It's something like a television operating in reverse.
To get color, you take multiple pictures with different filters in front of the camera for each one.