The search for hidden resources of power has lead humanity towards the development of magical arts in nearly every society where such searches have arisen. The sorcerers of a culture drive their minds deep into the fabric of the universe seeking greater control over their world. When the unpredictability of magic requires that the methods and theories of the art becomes standardized, religion develops.
A vision of reality to which one can relate on a personal level will much more easily gain acceptance than a vision of a world of nameless and incomprehensible forces. Fearing the responsibilities of power, religion allows desires to manifest through the "will" of a deity which acts as a filtration system. One prays to the deity, and the deity grants the desired favor if it does not interfere with the moral identity of the deity. By establishing deities representing the social functions of humans, a society limits the sort of magic done to that which the sanctioned deities will perform through their priests and devotees. This prevents blatantly disruptive sorcery and keeps things running in a relatively orderly manner.
The disadvantage of the system lies in that it creates distance between the magician and the magical act. As if the mind and its universe did not filter out enough of magic already, the theurgist volunteers for another censor (the deity) to monitor magical work. The loss of a direct contact with magical powers has inspired theurgists to search for alternatives through which deities can be moved to perform magic.
A general theory among theurgists holds that the gods created living things and endowed them with a force of spirit or soul which inhabits them, and that this soul has power, as it connects the creature to its creator. By releasing the soul of the creature, one releases its potential power - so the theory goes. Possibly after making note that the body dies when the blood leaves it, the ancient people of the world considered the spirit to leave with the blood, shedding its energy as the soul departs from the world of the living. After pacifying the deity who empowered the creature, the ancient theurgists would perform a ceremony to please the deity, during which they would slaughter the animal and release its energy for magical purposes. Often these rites were public rituals designed to release a burden from the population or to ensure success in their common goals. Sometimes, especially so in recent times, the slaughter serves a more personal or private end. In either case, as the prevalence of religion marks the degeneration of magic, so does the slaughter of animals in the name of sorcery represent the degeneration of behavioral standards and a mark of inefficiency.
I present the following not as an encouragement towards ritual slaughter, but as an explanation of the methods, uses, and cultural context of the acts.
Livestock are by far the most common sacrificial victims, and the reasons for their slaughter varies greatly. Generally this sort of sacrifice happens as a public act and receives the esteem of the community which it serves to bind.
Goats - After tying a ribbon about the throat of the animal and encouraging its erection, speak to it a special chant designed to liberate its soul and bring illumination upon all who eat its flesh. Sever the head with a sword. (a rite of kali)
Take two goats to the edge of a rock overlooking a trash heap. Announce that one shall bear the sins of the community, then toss it off the rock and into the burning trash. Set the other one free in the woods and instruct the people not to harm it. (Jewish rite of Atonement)
Kill a goat with a sharp knife consecrated to the purpose, and make a parchment scroll from its skin. (Solomonic Grimoires)
Cows or Bulls - Lay a hand on the head of the animal, asking forgiveness for some wrongdoing. Then cut its throat and collect the blood. Dip your fingers into it seven times, and sprinkle it on a veil covering the image of the deity. Put some of the blood in a censer, and pour the rest at the base of an altar to the deity. Burn the fat of the bull on the altar, and burn the rest of the carcass in a wood fire. (rite of reconciliation - Leviticus, Chapter 4)
Sheep or Rams - Similar to the ritual for bulls. Take the animal by the throat and slit horizontally while restraining it with ropes or strong men, if possible. Pour out the blood on the sides of an altar, and burn the rest after washing it. (also from Leviticus)
Pigs - The goddess Hecate, it is said, will take offerings of swine, if one puts the animal into a bag and buries it at a crossroads.
Chickens - Among the assorted blasphemies to reason and religion in the infamous grimoires, the sacrifice of a chicken is mentioned from time to time. In the Goetia, the brazen vessel's lid is consecrated with a libation of blood from a black cock, and in the Grimoire of Honorius, a perversion of the rites of Palm Sunday appears when the operator makes sigils on paper with the ashes of chicken feathers. In various Caribbean traditions (such as Santeria and Voodoo), chickens are sacrificed to encourage the satisfaction of the spirits invoked during ritual. The spirits feed on blood, and the participants spare themselves by offering the chicken's blood to the spirits. The blood of chickens (possibly due to the fact that one may easily obtain them) also commonly appears as a medium for scrying.
Dogs - Often looked upon with disdain as a sacrificial victim, the dog makes an ideal sacrifice for those deities who inspire infidelity and domestic quarrels. Remember that dogs have an instinctive "yelp" that they will make, however quickly you may kill them.
Cats - Stray cats run around all over any urban area, and so they receive perhaps the greatest torment from would-be diabolists. The methods vary widely - from slinging them onto rocks, cutting them open (watch for those claws!), or drowning. Only teenage varieties of Satanism has even remote support for the ritual sacrifice of cats, and these fellows might do better at petting the creatures than slaughtering them.
Exotic Animals appear almost exclusively in connection with specific procedures in sacrificial rituals. In this sense, the rites have a closer tie to sorcery than to theurgy, but the influence of religious rituals remains.
Rodents - Small creatures look furry in the pet department, but they can truly plague a home or farm. Perhaps out of frustration, the victims of such infestation can seek to remedy the situation by trapping the mice on a special mousetrap. The trap has symbols of binding on it, which forces the spirit of the mouse into servitude at the point of its death. The spirit of the mouse, according to the theory, goes to "nibble away" some obstacle.
Bats - Solomonic literature suggests using the blood of a bat to make certain occult symbols. One may obtain a bat while it sleeps, either during hibernation or during the daylight hours.
Reptiles and Amphibians - These animals are most often killed for their physical rather than magical properties, as in the case of species of frogs and toads which produce toxins for drugs or darts. The killing may be ritualistic and (especially in tribal settings where survival depends on hunting) show the power of the frog to bring success to the community, the efficacy is ensured by chemicals and not by gods.
Insects - Living things come in a fascinating variety, and one can only truly appreciate this variety if one has a special fondness for insects. Through the sacrifice of one insect (not a great loss, considering their numbers), others of the same species can be made to serve as a swarm, if given direction with magical words and signs.
Humans are considered a taboo for sacrifices, as most societies have considered this an act of antisocial behavior, except in the case of defeating an enemy.
Shrunken heads are made by taking a fresh human head and removing the skull, then boiling the skin and hair. The head is left to dry in the sun after this, and thereafter one fills the face with wax (to the desired facial shape) after sewing the eyes and lips shut. Sand fills the remainder of the head, and it can be stitched together along the scalp and neck.
Diabolists of ages past were accused of making ointments from human fat, to which they added deadly herbs such as nightshade and aconite. Likewise it is suspected that these same people made candles from boiled human fat, mixed with beeswax.
Today the diabolists may have more elaborate schemes in mind. Adrenaline-based compounds may be extracted from the adrenal glands with a small sponge, if one can keep the victim alive (and conscious) long enough for them to be terrified into releasing overdoses of adrenaline. A local anesthetic is most useful here. A simple bout with PCP might prove easier to obtain and more interesting, if one is inclined to such things. Also, one may extract dimethyltryptamine (DMT) from the human pineal gland, but a simple alkaline salt extraction will yield this chemical from canary grass with much less risk and much more efficiency.
If the death of a living creature releases some form of energy, it seems curious that no one decides to sacrifice fish, which are suitable food and which we catch in abundance. Also, if one considers the mere death-resistance maneuvers of the victim to empower the sacrifice, there seems little focus on it in the ancient methods.