The illustrations on this page show an enlarged section of a typical magazine illustration. The picture in the magazine was printed using inks in four colours—cyan, magenta, yellow and black. This process is called 4-colour printing or CMYK printing. (Here the K stands for blacK, because B usually stands for Blue.)
In 4-colour printing, each ink is applied as an array of small dots. (This array is sometimes called a half-tone screen, for historic reasons.) Each array is aligned in a different direction to reduce the chance of producing Moiré patterns, which would be distracting. The dots are spaced further apart on poorer quality paper such as newsprint because the ink spreads further in this kind of paper before it dries. (This spreading is called dot gain.)
The varying colours in the image are produced by varying the density of each ink. The final colours are produced by a fairly complex combination of processes but a simplified explanation will work well enough for most practical purposes.