mid-13c., peinten, "represent (someone or something) in paint;" c. 1300, "decorate (something or someone) with drawings or pictures;" early 14c., "put color or stain on the surface of; coat or cover with a color or colors;" from Old French peintier "to paint," from peint, past participle of peindre "to paint," from Latin pingere "to paint, represent in a picture, stain; embroider, tattoo," from a nasalized form of PIE root *peig- "to cut, mark by incision."
The sense evolution between PIE and Latin was, presumably, "decorate with cut marks" to "decorate" to "decorate with color." Compare Sanskrit pingah "reddish," pesalah "adorned, decorated, lovely;" Old Church Slavonic pegu "variegated;" Greek poikilos "variegated;" Old High German fehjan "to adorn;" Old Church Slavonic pisati, Lithuanian piešiu, piešti "to write." Probably also representing the "cutting" branch of the family is Old English feol (see file (n.2)).
From late 14c. as "represent persons and things in pictures or drawing, portray." To paint the town (red) "go on a boisterous or disorderly spree" is by 1884; to paint (someone or something) black "represent it as wicked or evil" is from 1590s. Adjective paint-by-numbers "simple" is attested by 1970; the art-for-beginners kits themselves date to c. 1953.