from my perspective, graphic design describes the process that happens before printing. and so to me, the printing isn’t really part of the graphic design. that is to say, doing the work of graphic design leads to have a graphic. what you do with the graphic is separate… the graphic could be printed, or it could be silk-screened onto a t-shirt, or posted on the web…
that said, there are a lot of ways to print an image. most modern printing methods are mostly just variations on the theme of the either the offset press or the inkjet printer, and i shall describe both. also i’ll describe silk-screening, which is pretty different but certainly counts as printing.
an offset press is a machine which uses a sheet of film called a “plate” to produce an image. the plate looks somewhat like a photograph or an x-ray, and was originally produced in very much the same manner, but can now be created using an ordinary laser printer. the plate is affixed to a roller which passes it through a tray of ink and then, once inky, rolls it against a piece of paper. the nature of the plate is such that the ink sticks only to the parts of the plate which represent the print image, and does not stick to blank sections. when the plate is rolled against the inked plate, the ink sticks to the paper, and comes off the plate, and voila, you have an image. if you do this four times with cyan, magenta, yellow, and black ink, you can create full-color images on the paper.
incidentally, this is basically how photocopy machines and laser printers work. a cylinder is given a static-electric charge on its surface which corresponds to the the image to be printed. then powdered toner is sprinkled on the drum, and sticks only to the charged parts. then the paper is heated and rolled over the drum, and the toner melts onto the paper.
ink jet printing is much simpler in operation, though it requires greater precision to design, build, and control an inkjet printer. what happens in ink jet printing is that a piece of paper is fed past either a single moving ink sprayer, or a row of many stationary nozzles. as the paper moves past, a computer controls the quantity of each color of ink to be sprayed.
silkscreening involves stretching a silk screen (often literally silk, but also often a synthetic substitute) over a frame, and then covering it with a gooey substance called emulsion which hardens when exposed to white light. naturally, you do this in a darkroom. you then take your image printed on acetate, and tape it over the screen, and then expose the whole apparatus to light. the image on the acetate blocks the light from exposing the emulsion under it, while the areas of the acetate which have no image allow light through, solidifying the emulsion. then you take away the acetate, wash the un-hardened emulsion off, and force ink through the screen onto your printing surface. the ink only passes through the areas which are not blocked by emulsion, and presto.
there are, naturally, a million different variations on these ideas, but hopefully you’re now able to get the gist of how printing works…