How should the sacrificial animal be divided? Is every part divided into thirds i.e. the liver into thirds, the head into thirds, etc…? How is it divided into thirds?

Sacrifice is a confirmed practice of the Prophet (peace and blessings be upon him) because he offered sacrifice and so did the Companions. He also said: "Three are obligatory upon me and voluntary for you; Sacrifice, witr, and duha" (recorded by Ahmed and al-Baihaqi).
Islamic law clarified how to divide and distrubute the sacrificial animal. It is recommended to divide the sacrificed animal into thirds; one third is eaten by the one doing the sacrifice, another third is given away as a gift, and the last third is given as charity. There is no harm if more than one third is kept, or given as a charity. This is because distributing the animal is recommended and not an obligation.
Ibn 'Umar (May God be pleased with them) said: "Sacrifice animals are divided [into three thirds]; one third for you, a third for your family, and a third for the poor."
The meat is the part of the animal which is distributed because it is the main objective, and is the part which benefits the poor and the needy. As for the innards such as the liver and other parts, it is recommended to divide them, though there is no harm if they are not. The head is not distributed but belongs to the person offering the sacrifice— it must not be sold or given to the butcher as payment.
It is obligatory to sacrifice an animal if one has vowed to do so, and the person offering the sacrifice may eat from it, give it away as a gift, and as charity to the poor and the needy.
Al-Qadi Abu al-Tayyib states that the Hanbali school maintains that it is impermissible for the owner of the vowed sacrifice animal to eat from it, which is the apparent meaning of the words of Imam Ahmed. Yet the relied upon opinion for this fatwa is that it is permissible for the one who made the vow to eat from the sacrificed animal. This is because sacrificing in itself is done to be eaten. The fact that the animal is slaughtered in fulfillment of a vow does not change anything except being an obligation.
God the Majestic knows best.