Each Shinigami has their own Zanpakutou that is unique to only them.
In the anime, Bleach, Shinigami use their Zapakutou to kill hollows, creatures that were once human souls but now eat souls. The Shinigami must release the human soul and send it to the Soul Society. They fight using four basic techniques.
Zankensouki
Zankensouki is the name for the four basic Shinigami techniques. Zan refers to Zanjutsu, or swordsmanship. Ken refers to Hakuda, or hand-to-hand combat. So is for agility, or hohou, and Ki refers to Kido, a form of magic.
Zanjutsu
Zanjutsu is the most common fighting technique for Shinigami. They use their Zanpakutou and sword fighting techniques to defeat the hollows and release the souls.
Hakuda
Hakuda is hand-to-hand combat. Most of the Shinigami do not use this technique because of the dangers. The Onmitsukido, or Secret Mobile Corps, specialize in Hakuda.
Hohou
Hohou is the Shinigami's agility technique. Shinigami can learn a technique called shunpo, which will make them move faster than the eye can see, and giving them the upper hand in battle.
Kidou
Kidou is the "demon arts", a form of magic used only by Shinigami. Kidou can be used to attack the enemy, and is called hadou. Kidou can also bind a target, heal the wounded, and defend. This is called bakudou.