The Ghost was able to possess an opponent's monsters once per turn. If the opponent attempted to attack with the possessed monster, the attack would be negated and they would take damage equal to half the monster's ATK, while the controller of "Dark Sanctuary" would gain that amount of Life Points. As evidenced by Yugi's activation of "Collected Power", the Ghost was apparently treated as an Equip Card equipped to the possessed monster.
Yami Bakura used "Dark Sanctuary" against Yami Yugi in the Battle City finals, combining it with "Dark Spirit of the Silent" to force Yugi to attack with the possessed monsters. Bakura himself had no control over which monster the Ghost possessed and it acted of its own accord. He was able to see which monster the Ghost possessed, but Yugi could not.
Yugi was able to destroy the Ghost once by using "Collected Power" to force the Ghost to possess "Kuriboh", followed by "Exile of the Wicked" to destroy "Kuriboh" and subsequently the Ghost. Another time, he was able to avoid the Ghost through Summoning the Egyptian God "Slifer the Sky Dragon", who was immune.