The Hebrew word korban is built on the root that means to draw near, and in its causative sense to bring near. What the noun names is therefore the act of presentation, not the act of slaughter, and the classes set out in the opening chapters of Leviticus are distinguished by what is brought, who eats it and what the bringing is for. The manner of killing is nearly identical across them and carries almost none of the weight.
An animal offering moved through a fixed sequence. The offerer brought the beast to the entrance of the sanctuary court, leaned both hands on its head, and it was slaughtered, on the north side of the altar for the graver classes and beside it for the rest. From that point the priests took over. They caught the blood in a vessel and applied it to the altar in the manner the class required, flayed and jointed the carcass, washed the entrails and the legs, and arranged the parts on the altar fire in an order the later sources record in detail.
Not every korban was an animal. Flour, oil, frankincense and wine were brought in their own right and also as the standing accompaniment of the public animal offerings, and at the spring and summer festivals sheaves and loaves were presented. A person who could not afford a beast discharged the same obligation with a pair of turtledoves or young pigeons, or in the poorest case with a measure of flour, and the text says so in the same breath as the more expensive options rather than as a concession appended afterwards. A single festival day could therefore see public and private, obligatory and voluntary, animal and vegetable offerings on the same fire.