"perform, execute, achieve, carry out, bring to pass by procedure of any kind," etc., Middle English do, first person singular of Old English don "make, act, perform, cause; to put, to place," from West Germanic *doanan (source also of Old Saxon duan, Old Frisian dwa, Dutch doen, Old High German tuon, German tun), from PIE root *dhe- "to set, put, place."
Use as an auxiliary began in Middle English. Sense of "to put, place, lay" is obsolete except in phrases such as do away with. Periphrastic form in negative sentences (They did not think) replaced the Old English negative particles (Hie ne wendon).
Meaning "visit as a tourist" is from 1817. In old slang it meant "to hoax, cheat, swindle" (1640s). Slang meaning "to do the sex act with or to" is from 1913.
Slang do in "bring disaster upon, kill" is by 1905. To have to do with "have concern or connection with" is from late 13c. To do without "dispense with" is from 1713. Expression do or die indicating determination to succeed despite dangers or obstacles is attested from 1620s.
Compare does, did, done.