Middle English turnen, from late Old English turnian "rotate, revolve; move about an axis, center, or fixed position," also in part from Old French torner, tornier, Anglo-French turner "turn away or around; draw aside, cause to turn; change, transform; turn on a lathe" (Modern French tourner).
All are from Latin tornare "to polish, round off, fashion, turn on a lathe," from tornus "lathe," from Greek tornos "lathe, tool for drawing circles" (reconstructed in Watkins to be from PIE root *tere- (1) "to rub, turn").
From late 12c. as "change position or orientation so as to face or point in a different direction," hence "change course, go in a different direction." In reference to the tide, etc., "reverse course or direction," c. 1300.
Transitive senses in English are from c. 1200 as "cause to shift so as to face in a different direction;" by c. 1300 as "cause a change of course." Related: Turned; turning.
Many figurative senses and expressions (turn (something) into (something else)) likely grew from the notion of "shape (something) while rotating it on a lathe or wheel, form or fashion (a piece of wood or metal) with a chisel while the object is rotated," the classical sense, attested in English by mid-14c. "Execute in round outlines," hence "form, fashion, or shape in any way" (1610s).
From late 12c. as "cause to undergo transmutation from one substance to another." Hence "change in a character or property" (color, thickness, mass, etc.), c. 1300, also transitive. The sense of "become sour or tainted" is by 1570s.
Also from late 12c. as "lead to" (grief, advantage, etc.), "result as a consequence of;" from c. 1200 as "come to pass, happen, occur." Also from c, 1200 as "become inverted, assume a reverse or contrary position;" also "repel" (evil, danger); "rout in battle." By c. 1300 as "shift allegiance, shift loyalties, change sides," also transitive.
To turn down (v.) "reject" is recorded by 1891, American English. To turn in "go to bed" is attested from 1690s, originally nautical. Turn to "look to for help or hope, have recourse" is from late 14c.
To turn the stomach "nauseate" is recorded from 1620s. To turn (something) loose "set free" is recorded from 1590s. To turn up one's nose as an expression of contempt is attested from 1779.