Old English sceotan "to shoot" (class II strong verb; past tense sceat, past participle scoten), from Proto-Germanic *skeutanan (cf. Old Saxon skiotan, Old Norse skjota, Old Frisian skiata, Dutch schieten, German schießen), from PIE root *skeud- "to shoot, to chase, to throw, to project" (cf. Sanskrit skundate "hastens, makes haste," Old Church Slavonic iskydati "to throw out," Lithuanian skudrus "quick, nimble").
Meanings "send forth swiftly" and "wound with missiles" were in Old English. In reference to pool playing, from 1926. Meaning "to inject by means of a hypodermic needle" is attested from 1914. Meaning "photograph" (especially a movie) is from 1890. As an interjection, an arbitrary euphemistic alteration of shit, it is recorded from 1934. Shooting star first recorded 1590s. Shoot the breeze "chat" first recorded 1941. Shoot to kill first attested 1867. Shoot-out (n.) is from 1953.