Samurai sword, or katana, fighting lessons can be divided up into three main schools of martial arts. They are kenjutsu, kendo and iaido. These three forms of are the three fundamental styles of katana fighting, and all emphasise a different aspect to fighting with a katana. For all of these styles you will need certain equipment. This equipment varies between styles, and if you decide to take up lessons in any of these martial arts, ask your sensei which equipment he recommends.
Kenjutsu is one of the earliest forms of katana fighting techniques, with its origins from about AD 800. Taking up kenjutsu would be useful in understanding the origin of katana sword fighting and learning the basic techniques associated with katana fighting styles. Kenjustsu literally means "the art of the sword." Kenjutsu is a highly combative form of katana fighting and is centred on the actual fighting techniques. The techniques in kenjutsu always begin from a position where the sword has already been drawn.
Kendo is an expansion of the earlier form kenjutsu and was developed to increase knowledge of sword fighting techniques and improve upon those that already existed. As opposed to kenjutsu, kendo is less combative and is focused more on improving the mind of the martial artist instead of strictly improving his sword skills. Kendo is mainly a competition sport and it is practised using practice swords made out of bamboo shoots.
Iaido is a younger form of katana fighting styles than kenjutsu and is believed to have its origins in around AD 1200. The main difference between iaido and kenjutsu and kendo is that iaido techniques usually begin with the sword still in its scabbard, as this is an everyday sort of starting position and the swordsman must learn to draw quickly and deliver a fast blow from an unready position.
The equipment needed for these katana fighting styles will differ among styles. One basic tool for any of these is what is known as a bokken, or a wooden practice katana. For kendo you will need a bamboo practice sword known as a shinai. For all of these arts you will also need to acquire budogu or body armour, which consists of a heavy apron, face mask, throat guard, gloves and gauntlets.