Hanging was a form of capital punishment by which an individual was suspended in the air by a rope, usually tied at one end into a knot called a "noose".
To effect a hanging, the rope was affixed to a tree, beam or other fixed point, and the noose was tightened around the victim's neck. Then, the victim was pulled up, or support dropped from underneath him, until his entire body weight was being borne by his neck.
Death would subsequently result from strangulation or the neck's inability to bear the weight of the victim.
When in 2369 Constable Odo faced the chages of murder, he was hunted down by an angry mob into his security office. Commander Benjamin Sisko tried to calm down the situation and asked what the angry people want to down with Odo. Zayra answered, "He's right. Might be hard to get a rope around the neck of a shapeshifter...." (DS9: "A Man Alone")
The Bajoran Kainon told Constable Odo that he wanted to be informed when they hang the Cardassian prisoner Aamin Marritza. (DS9: "Duet")
In 2374, during the Dominion occupation of Deep Space 9, Vedek Yassim organized a demonstration on the Promenade. Yassim appeared on the upper promenade level and exclaimed "Evil must be opposed," before she stepped off the second level with a rope around her neck, hanging herself. (DS9: "Rocks and Shoals")
Notable hangings
On the Skagaran colony in 2153, a Human posse led by Deputy Bennings hung a Skagaran for alledgedly killing a man named Clay Stanton. (ENT: "North Star")
On the unnamed planet inhabited by Gosis' species, hanging was the preferred method for carrying out the death penalty. (ENT: "The Communicator")
As part of a conviction for fraud, Deneb V offered a guilty party the choice of death sentences, one was death by hanging. (TOS: "I, Mudd")
Trelane once held a mock trial of James T. Kirk on Gothos, where he issued the verdict that Kirk would "hang by the neck until" Kirk was "dead, dead, dead." (TOS: "The Squire of Gothos")
After her crew voluntarily chose to disobey her orders in 2375, Kathryn Janeway remarked that they could all be "hanged for mutiny," a reference to the ancient naval custom of hanging mutineers. (VOY: "Night")