Menachos, chapter 9, mishnah 8. We continue with the laws of semichah (leaning on the animal), and the mishnah opens: "Hakol somchin chutz mecheresh shoteh v'katan" - everyone performs semichah, except for those disqualified who are listed here.
Those who are disqualified from semichah:
A cheresh, a shoteh and a katan - the familiar trio of those who lack da'as (mental competence). The cheresh is one born without the ability to hear or speak; the shoteh is one impaired in his mind, who does not understand the consequences of his actions; the katan is a boy who has not yet reached the age of thirteen and has not grown two hairs. Since they lack da'as, they are exempt from all the mitzvos, and therefore they do not perform semichah.
A blind person - one who is blind in both eyes. This law is derived through a gezeirah shavah from the Sanhedrin and from the leaning of hands on the bull brought for a communal error: just as members of the Sanhedrin cannot be blind, so too one who performs semichah cannot be blind.
A non-Jew - a gentile who brings an olah does not perform semichah, as it says "Speak to the children of Israel" - the obligation of semichah applies to them and not to gentiles.
An agent - one sent as another person's agent to bring his offering does not perform semichah, as it says "his hand" - the hand of the owner and not the hand of the agent.
A woman - as it says "Speak to the children of Israel," and the Sages expounded: the sons of Israel and not the daughters of Israel.
A slave - a Canaanite slave, who is not Jewish. His law is derived from the comparison that equates him with a Jewish woman regarding obligation in mitzvos.
At first glance one should ask: how does a cheresh, shoteh or katan come to bring an offering in the first place? After all, they cannot consecrate an offering, since they lack da'as.
The answer emerges from the previous mishnah: a person can become obligated in an offering through inheritance, for when he inherits his father's consecrated animal it falls upon him to bring it. In the previous mishnah we learned that an heir does indeed perform semichah, but if the heir is a cheresh, a shoteh or a katan - he is obligated to bring the offering, and nevertheless he does not perform semichah, because he lacks da'as.
"U'semichah shiyarei mitzvah":
Semichah is an accompanying mitzvah, and it does not hold up the offering itself. If a person did not perform semichah for whatever reason, this does not detract at all from the validity of the offering: the sacrifice is rendered fit through the placing of the blood on the altar, and the absence of semichah does not prevent the offering from accomplishing what it is meant to accomplish.
How semichah is performed - "al harosh bishtei yadayim":
Semichah is performed on the animal's head, and ideally between its horns, if its head is large enough. The one performing semichah takes both of his hands - not one but two - and presses with all his strength on the head of the animal. At that moment he recites the confession when bringing the offering, and according to the Rambam, with a shelamim or a todah offering he offers praise to Hashem at that time.
Although in the passage dealing with semichah it says "v'samach yado" - "and he shall lean his hand" - in the singular, in the passage of the goat sent away, the goat to Azazel on Yom Kippur, it says "v'samach Aharon es shtei yadav" - "and Aharon shall lean both his hands": Aharon, who is the Kohen Gadol, places both of his hands on the head of the goat. From there we learn that it is two hands that press on the head of the animal.
"U'vamakom shesomchin sham shochtin":
In the very same place where the semichah was performed, the slaughtering must be done - at that exact spot in the Azarah. It is as though the animal's feet are not to move from their place, and immediately after the semichah the slaughtering is performed.
Take, for example, an animal that must be slaughtered on the north side of the Altar, such as an olah: the owner enters the Courtyard, passes through the Courtyard of the Kohanim, and comes to the northern section of the Courtyard, performs semichah there, and ideally the slaughter takes place immediately afterward. And if for some reason that did not happen - the animal ran off or moved from its place - this does not invalidate anything, since we have already learned that semichah itself is not indispensable.