What is jutsu
Jutsu literally mean art or skill in English (see name dictionary) and is a term more popularly linked to the traditional fighting methods of the samurai. To apply it in the world of Naruto, to say something no jutsu' would mean something like 'the art (or skill) of something'. For example, kage (shadow) bunshin (replication) no jutsu would literally mean the 'skill of shadow replication'. 'Jutsu' is sometimes confused with 'jitsu', which means fighting art. But since meanings of the 2 words are similar, I guess it doesn't matter. Just wanted to clear that up so you don't get into arguments about whether it's 'jutsu' or 'jitsu'.
Hand seals are making signs with your hands. The seals consist of mixing and matching the basic oriental 12 astrological signs - Rat, Bull, Tiger, Rabbit, Dragon, Snake, Horse, Sheep, Monkey, Rooster, Dog, Boar.
Ninjutsu in reality is the art practiced by the ninjas of feudal Japan. In the Naruto world, ninjutsus are like magic tricks where you can make yourself disappear or turn sexy, or clone yourself and the works by forming hand seals
Taijutsu can be called Body Art and is a term used to describe hand-to-hand combat without the use of weapons, just your body. No hand seals are required for Taijutsu as you only have to depend on your strength and speed.
Genjutsu in the Naruto world is a kind of technique to attack your enemy by casting illusions. For example, making them believe they are attacked by a hoard of tigers or showing them illusions of their comrades falling. Genjutsus are also activated by hand seals.
Kinjutsu in the Naruto world are the forbidden techniques where those who cast the jutsu might put their life at risks. The forbidden fruit is always the most tasty though so these dangerous techniques are sought after by baddies.