The Method of Slaughtering an Animal
They are: the air passage, the gullet, and the two jugular veins which are on either side of the gullet and the air passage. If only three out of these four are cut, the slaughter will be valid and the animal will be halaal. If only two of the four are cut, the animal will be considered to be dead and it will not be permissible to consume the meat of such an animal.
At the time of slaughtering the person intentionally did not take the name of Allah (سبحانه و تعالى). The animal will be considered to be dead and it will be haraam to consume it. But if a person forgets to take the name of Allah (سبحانه و تعالى), the animal will be halaal.
It is makruh to slaughter an animal with a blunt knife as this causes much suffering to the animal. It is also makruh to begin skinning, cutting, breaking the hands and feet of the animal before it can become cold (meaning, before it can become lifeless). Similarly, it is makruh to continue cutting the animal's neck after having cut the four passage ways.
At the time of slaughtering a fowl, it's entire neck got cut off. It is permissible to eat such a fowl, and not makruh. However, it is makruh to slaughter the fowl in such a manner, although consuming it is not makruh.
Slaughtering of an animal by a Muslim is permissible under any condition. This is irrespective of whether the Muslim is a male, a female, in a state of purity or in a state of impurity. In all conditions, an animal slaughtered by a Muslim is halaal. An animal slaughtered by a non-Muslim is haraam.
It is permissible to slaughter an animal with any sharp object such as a sharp stone, a sharp cane, a sharp bamboo, etc.