Hung is both the form and the past participle of hang (as in hang up a telephone) so you can say:
(a) I hung up the phone.
(b) I hung up.
In this use as in sentences (a) and (b) above hang up is a separable phrasal verb.
Hang is also used as a transitive verb to mean the same as hang up as in sentences (c) to (e) below:
(c) Nancy hung her clothes in her closet.
(d) You hung the pictures wrong!
(e) The pictures were hung on the wall with great care.
Hang is also an intransitive verb as in (f) and (g):
(f) The clothes hung on the clothesline frozen stiff in the cold.
(g) The picture hung crookedly from one of its hooks; the other hook had fallen away.
The other past form of hanghangedis the past or past participle of hang. It is used to refer to the execution of a person by hanging a rope around the neck as in (h) and (i):
(h) They hanged the ax murderer.
(i) The ax murderer was hanged.
Fortunately hanged is used much less frequently than hung.