In general, the sacrificial animal for sin offerings depended on the status of the sinner offering the sacrifice; for a high priest or an entire community, the sacrifice was to be of a young bullock; for a king or a prince the offering had to be a young male goat; for other individuals the offering had to be either a young female goat, or a female lamb; for poor individuals unable to afford these, a turtle dove sufficed. Like the other types of sacrifice, the sacrificial animal had to be completely unblemished.
Apart from such general offerings for unintended sin, sin offerings were always given:
The ritual of the sin offering began with the offerer(s) confessing their sins over the head of the victim. In the case of community offerings the elders performed this function, in the case of Yom Kippur, the high priest performs this task. The animal would then be killed by the offerer, or the priest if the offerer preferred, and the blood carefully collected by Levites in an earthen vessel. In the case of sacrifices at the Temple in Jerusalem, some of the blood would be sprinkled in front of the veil covering the entrance to the Holy of Holies, except on Yom Kippur, when the blood would be sprinkled in front of the mercy seat; this was done seven times. The remainder of the blood was poured out at the base of the altar, and the earthen vessel that had contained it would be smashed, while the fat, liver, kidneys, and caul, were burnt on the altar.
The flesh was later consumed by the priest and his family, except when the priest himself was among the offerers (such as in community offerings, and in the case of Yom Kippur), when it would be burnt outside the sanctuary. According to textual scholars these rules originate from two different layers in the Priestly source, thought by scholars to be one of the source texts of the Torah; the Priestly code within the priestly source is believed to be a series of additions to the text, from Aaronid editors, over a large period of time. The earlier source is thought to be the one referring to the flesh being consumed by the priests, while the later source reflects a development where the flesh from sin offerings was seen as insufficiently holy and thus needing to be disposed elsewhere. In the Book of Hosea, a reference to the earlier form suggests a possible reason for the change - the priests were accused of rejoicing in the people's wickedness as they were living off the sin offerings.
When the sacrificial animal was a bird, however, the ritual was quite different. The bird was slaughtered by a thumb being pushed into its neck, and the head being wrung off. A second bird would then be burnt on the altar as a whole sacrifice, completely immolated by fire.
Although known as sin offerings, it is more likely that such offerings began as offerings made for unintentionally breaking a taboo (here meaning something which is seen as sacred but simultaneously prohibited). The offerings for recovery from discharges and childbirth being for the breaking of a taboo about contact with blood - pus potentially containing blood, menstruation obviously containing it, and in the case of childbirth blood comes with the placenta. Textual scholars believe that the biblical regulation specifying the offering for childbirth originally fell among those concerning bodily discharges (due to various textual features), and hence that childbirth was treated as a form of abnormal discharge, for which a period of recovery was required.
The Nazarite's offering being due to the breaking of the Nazarite's own taboo nature, due to consecration to the deity, when the Nazarite vow was terminated. Tzaraas was seen as a disease inflicted by God, as punishment for transgression of mitzvot, and hence people becoming inflicted with Tzaraas themselves being seen as taboo (thus being temporarily expelled from society as a result); the sin offering for recovery from Tzaaras, for which the same sacrificial animal as the Nazarite's sin offering is proscribed, being due to the breaking of this taboo state by the act of recovering.
The Yom Kippur sin offering is considered to have developed slightly later; the biblical text seems to explain this offering as being for the purpose of protecting the high priest from death (...so that he does not die) when he approached the mercy seat, an action which was taboo (as the mercy seat was seen as sacred, but approach to it was prohibited). The passage in which this is explained as being about atonement for real sin, rather than just breach of this taboo, being considered by textual scholars to be a later gloss added to the text. The sin offering required when a priest had sinned, for which there is a similar sacrificial animal as the Yom Kippur offering, is considered by scholars to be a much later development, and only added to the text of Leviticus in the latest stages of its compilation, after sin offerings had begun to be seen as being about atonement for actual sin rather than relatively immediate breaches of taboos.
The other sin offerings are considered by scholars to be represent gradual developments; from being offered after contact with unclean animals, which is more of a taboo, to being offered for ritual uncleanliness in general, and finally to being offered for arbitrary sins. The gradations, according to which the type of sacrificial animal depends on the social status of the sinner, are considered by textual scholars to also be a later development, from a similar period of time as these offerings for actual sin.