Sincerity To Allah
The 'aqiqah must be offered purely and sincerely to Allah offering a sacrifice to other than Allah is a major sin and act of shirk. Those who commit it would be liable to Allah's wrath and curse.
Using a sharp knife
Slaughtering the animals should be done quickly and skillfully, using a sharp knife.
Mercy Toward The Animal
Out of Allah's great and boundless favors on us, he subjugated some animals for our sustenance. Thus, the animals should be slaughtered with a sense of Mercy and compassion. This includes hiding the knife from the animal's sight until the last minute, and avoiding killing the animals within each others' sight.
Laying The Animal Down
It is recommended to lay the animal down before slaughtering it (except for Camels 🐫.)
Cutting The Throat
We have seen from Rafi's earlier Hadith (p, 78) that one of the requirements of correct slaughtering is that the blood should be poured out. This is done by cutting the throat.
Pronouncing Allah's Name
It is required to pronounce Allah's name over an animal while slaughtering it.
Even for a sheep🐑 or goat, show it Mercy while slaughtering them, Allah will show mercy to you also.