Ichigo's sword makes its first appearance in episode 2 of the anime, and chapter 1c of the manga. It has the basics of a normal zanpakutou, that being a standard katana, but it is massive in size. The size of this zanpakutou is a result of Ichigo's inability to control his reiatsu, and thus the blade ends up being just as big as him.
Ichigo's zanpakutou appears for the first time after Ichigo takes Kuchiki Rukia's Shinigami powers, after the instantaneous severing of the attacking Hollow's arm. The size of the zanpakutou startled Rukia, who had never seen one of such size, giving reference to Ichigo's immense reiatsu.
This sword served as Ichigo's primary weapon until it was shattered by Kuchiki Byakuya, who had come to the Material World to bring Rukia back to Soul Society to recieve the death sentence for giving her Shinigami powers to a human.
Ichigo's zanpakutou's ShiKai makes its first appearance as a sword in chapter 67, and episode 20. Prior to this, Ichigo's zanpakutou revealed itself to Ichigo in a human form only Ichigo could see in manga chapter 63 and anime episode 19.
While training with Kisuke Urahara, Ichigo calls upon the ShiKai form of his zanpakutou, revealing its name to be Zangetsu(moon cutter). The sword is still very large, though not as large as its original form. It is pointed out by Junta, one of Urahara's shopkeepers, that Zangetsu lacked both a hilt and a hand-guard. It has the appearance of a large, black cleaver, with the curve of a katana. Zangetsu has no sheath, and is usually wrapped in cloth which remains tied to the handle during use.
So far, Zangetsu has revealed one ability to Ichigo, that being the Getsuga Tenshou (Moon Fang Sky Charge). The Getsuga Tenshou is a dense blast of reiatsu released from Zangetu's blade during a slash, or fired from the tip of the blade as though it were a gun. It also appears that Ichigo has the ability to manipulate the shape of the Getsuga Tenshou depending on the manner in which it is used.
Ichigo's BanKai, though most train for ten years, was achieved in 3 days, with the help of Yoruichi and the method created and used by Kisuke Urahara in his underground cavern in Soul Society. Ichigo fought against the human form of Zangetsu for the forementioned three days, using various swords which resembled Zangetsu.
Zangetsu's BanKai is unusual compared to most other BanKai. The BanKai of most zanpakutou tends to be very large, due to the massive about of reiatsu used to form it and use it. Ichigo's BanKai, Tensa Zangetsu(Heavenly Chain Moon Cutter), is a black katana of normal size. Attached to the hilt of the sword is a short black chain. The hand-guard is a manji, a backwards swastika.
Tensa Zangetsu gives Ichigo incredible speed, such that it surpasses the "Flash Step", a running technique said to be the fastest in Soul Society. This is due to the BanKai actually sealing up all of his unstable spiritual energy explaining why his his katana is so small compared to his ShiKai and Zanpakutou in sealed state. The downside of this is that Ichigo has yet to fully master his BanKai, and as such, it tires him after using it for a good duration, causing his speed to reduce.
Tensa Zangetsu also has the ability to fire a Getsuga Tenshou, though it is colored black instead of blue like the ShiKai form of the attack. This attack in BanKai form is called "his technique" by Ichigo, in reference to the Hollow which resides within Ichigo. Multiple uses of this technique causes Ichigo to lose control to his Hollow side.