hang (n.) Look up hang at Dictionary.com
late 15c., "a sling," from hang (v.). Meaning "a curtain" is from c.1500; that of "the way cloth hangs" is from 1797. To get the hang of (something) "become capable" is from 1834, American English. Perhaps originally in reference to a certain tool or feat, but, if so, its origin has been forgotten. It doesn't seem to have been originally associated with drapery or any other special use of hang.
'To get the hang of a thing,' is to get the knack, or habitual facility of doing it well. A low expression frequently heard among us. In the Craven Dialect of England is the word hank, a habit; from which this word hang may perhaps be derived. [John Russell Bartlett, "Dictionary of Americanisms," New York, 1848]
hang (v.) Look up hang at Dictionary.com
a fusion of Old English hon "suspend" (transitive, class VII strong verb; past tense heng, past participle hangen), and Old English hangian (weak, intransitive, past tense hangode) "be suspended;" also probably influenced by Old Norse hengja "suspend," and hanga "be suspended." All from Proto-Germanic *hangen (intransitive) "to hang" (cognates: Old Frisian hangia, Dutch hangen, German hängen), from PIE *konk- "to hang" (cognates: Gothic hahan, Hittite gang- "to hang," Sanskrit sankate "wavers," Latin cunctari "to delay;" see also second element in Stonehenge). As a method of execution, in late Old English (but originally specifically of crucifixion).

Hung emerged as past participle 16c. in northern England dialect, and hanged endured only in legal language (which tends to be conservative) and metaphors extended from it (I'll be hanged). Teen slang sense of "spend time" first recorded 1951; hang around "idle, loiter" is from 1830, and hang out (v.) is from 1811. Hang fire (1781) was originally used of guns that were slow in communicating the fire through the vent to the charge. To let it all hang out "be relaxed and uninhibited" is from 1967.