Suigetsu can change his shape at will, generally to help in his skills, and when left unconscious, he is reduced to a jelly-like condition. When he is observed recuperating from these unconscious phases, he is placed in a big tank of water and takes on the appearance of a fish.
Suigetsu has always been a bit of a mystery character. He lives at the Dragon Palace with Gennosuke, who inherited the ability from their father, Musashi. It's possible that both boys were adopted by Musashi so he could have two sons with the same ability. However, it's more likely that they were born to normal parents and then given this power to make them equal to Goda Yumi, the wife of Musashi.
In most cases, the main characters are Kenji and Kojiro, two friends who find themselves facing off against one another in battle. However, other characters such as Togo Igawa, Miyamoto Musashi, Oishi (who was once married to Gennosuke's sister), Hattori Hanzō, and even Gennosuke himself may appear from time to time.
Musashi started out his life in Japan looking for someone who knew him well enough to tell if he was really the son of Iha Isami or not. This was done so he could prove to everyone that he was indeed the true heir to the Baito style of swordsmanship.
Suigetsu is composed entirely of water. Obviously, you electrocuted him to death. Alternatively, he may use fire to deplete all of the oxygen in his body. Water is composed of H2O, hydrogen, and oxygen. Oxygen is an element. It cannot be destroyed, only transformed from one state to another.
Suigetsu's death will also appear in the final episode of Naruto Shippuden. In this scene, after being defeated by Sasuke Uchiha, Naruto tries to help his friend. However, due to his weak condition, Suigetsu falls into a puddle of water that has been left behind by Sasuke and disappears under the surface of the liquid. Since water is essential for life, this means that Suigetsu has been completely removed from the world of the living.
There are several other characters who we know will die during the course of the series. Here are just a few of them:
Kakashi Hatake - Killed by Madara Uchiha with his own hand weapon. Before he dies, he tells Obito to kill Kakashi's successor as well as himself.
Tsunade - Shot dead by an assassin hired by Sasori. After her death, Sasori is seen crying over her body.
Sasuke Uchiha - Killed Suigetsu.
Suigetsu noted one of the medical-nin was in a stupor when they arrived to begin their testing (unaware he was being controlled by Sasuke's Sharingan). The medical-nin then unlocked Suigetsu's chamber, freeing him from the base. Soon after, he was being hunted by Sasuke and Karin. Forced to fight, Suigetsu defeated both men.
During the Fourth Shinobi War, Suigetsu is assigned to protect Danzō Shimura from an unknown enemy. When Shimura is captured, it's revealed that this enemy is actually Hashirama Senju, who plans to use his DNA to revive his son, Naruto. Filled with rage over this betrayal, Suigetsu attacks the old man but is stopped by Taka Hagane. After Hagane dies trying to protect Shimura, Suigetsu decides to follow him into death without fear or regret. Before he can be killed by Naruto, however, Hashirama uses his last bit of energy to clone another copy of himself which he gives to Suigetsu before dying. This new version of Suigetsu vows to kill Naruto because he believes he is responsible for his master's death.
Two years later during the Fifth Shinobi War, Suigetsu joins forces with Sasori to destroy the village where Naruto lives. After killing many villagers including Naruto's mother, Sarada Uchiha, they are confronted by Konohagakure's top ninja team led by Tsunade.