Yevamos, Chapter 12, Mishnah 6. This Mishnah walks through the precise procedure of the chalitzah ceremony itself.
Coming to beis din and the judges' advice:
How is the mitzvah of chalitzah performed? "Ba hu vivimto l'veis din" - the yavam and his yevamah come together to beis din, "v'hem masi'in lo eitzah hahogenes lo" - the court gives him the advice that is appropriate for him. For example, if he is a young man and she is an older woman, or if he is elderly and she is young, they tell him that it is preferable to perform chalitzah rather than yibum, since such a marriage is unlikely to succeed. As the verse states: "V'kar'u lo ziknei iro v'dibru eilav" - the elders of his city shall call him and speak to him, and they discuss with him what the right and fitting course of action would be.
The declarations that precede the chalitzah:
"Me'ein yevami l'hakim l'achiv shem b'Yisrael" - she says: my yavam refuses to establish a name for his brother in Israel, he does not wish to perform yibum and does not wish to be the yavam.
"Lo chafatzti l'kachtah" - and he confirms it and says: I do not wish to take her.
These two declarations are direct quotations from the passage in the Torah, "uvilshon hakodesh hayu omrim" - they must be said in Hebrew, in the original language of the Torah.
The act of chalitzah:
"V'nigshah yevimto eilav l'einei hazekeinim" - the yevamah approaches him and draws near, before the eyes of the elders.
"V'chaltzah na'alo me'al raglo" - she removes his shoe from his foot.
"V'yarkah b'fanav" - she spits before him. And the Mishnah specifies: spittle that is visible to the judges - the judges must be able to see the spittle.
"V'ansah v'amrah":
The Mishnah continues and quotes from the Torah: "V'ansah v'amrah: kachah ye'aseh la'ish asher lo yivneh es beis achiv" - this is the text she must recite. On this the Mishnah comments: "Until here they would read to her" - up to this point in the passage they read to her, meaning they tell her to say these words. And beis din is very careful about her precise and correct pronunciation of every word.
"And when Rabbi Yochanan read to a woman beneath the oak tree in Kfar Eitam and completed the entire passage, they established the practice of completing the entire passage" - when he read to her beneath the oak tree in Kfar Eitam, he had her complete the whole passage and read the continuation of the verse as well. From that time on it was established that the entire passage must be finished, and she also recites: "V'nikra shemo b'Yisrael beis chalutz hana'al" - and his name shall be called in Israel, among the Jewish people: the house of the one whose shoe was removed. Even though the Tanna Kamma did not say that she must recite this, Hyrcanus established this declaration as the accepted practice.
A mitzvah upon the judges:
The Mishnah notes that this declaration is "a mitzvah upon the judges" - even though it was established that she too says it, the primary obligation rests upon the judges to say it. "And it is not a mitzvah upon the students" - it is not an obligation upon the students who happen to be sitting there, but rather upon the judges to say it.
Rabbi Yehudah disagrees and says: "It is a mitzvah upon all who are standing there to say: chalutz hana'al, chalutz hana'al, chalutz hana'al" - three times they declare that the shoe has been removed. It is possible that Rabbi Yehudah is not actually disagreeing, but is raising a separate point: all those standing there do not recite the entire verse "v'nikra shemo b'Yisrael," but only the final words - "chalutz hana'al" - three times.
In summary: In this Mishnah we learned the order of the chalitzah ceremony and its stages: bringing the yavam and his yevamah to beis din and the fitting advice of the elders; her declaration "me'ein yevami" and his declaration "lo chafatzti l'kachtah" in Hebrew; the act of chalitzah - the approach, the removal of the shoe and the spitting that is visible to the judges; the recitation of "kachah ye'aseh la'ish" and the completion of the entire passage through "beis chalutz hana'al"; and the dispute among the Tannaim as to whether the declaration rests upon the judges alone, or whether all those standing there also say "chalutz hana'al" three times.