Yoma, Chapter 3, Mishnah 4. Our Mishnah describes how the Kohen Gadol's first immersion took place, and then goes on to list the order of the morning services that followed.
"Parsu sadin shel butz beino u'veineihem":
They would spread out a partition - a large sheet of butz, that is, of linen - between him and the people who were standing there, the entire crowd that was waiting at the site. In this way a partition was made for him, in whose shelter he could undress.
And why specifically of linen? Because all of the unique services of that day were performed in bigdei butz - the linen garments that the Kohen Gadol wore on Yom Kippur specifically, and not his regular garments. Therefore, as a reminder of this, the sheet that surrounded him was also made of linen.
The immersion and the dressing:
"Pashat" - he removed his garments, which were his own personal clothing.
"Yarad v'taval" - he went down and immersed in a mikvah.
"Alah v'nistapeg" - he came up and dried off the remaining water.
"Heiviu lo bigdei zahav" - the first services he was about to perform, among them the tamid, are not unique to Yom Kippur, and therefore he put on the golden garments - the eight items that the Kohen Gadol wears throughout the year.
"V'lavash" - he put them on and was clothed in them.
"V'kidesh yadav v'raglav" - he sanctified his hands and feet after putting on the garments, since every putting on and removing of garments requires sanctification of the hands and feet.
The service of the tamid:
Now, once he was dressed and had sanctified his hands and feet, they brought him the tamid - the animal for the daily offering. And what did he do? "Keratzo" - he performed the initial part of the slaughter. He did not complete it, but rather slaughtered enough for the slaughter to be valid, and did not finish cutting through the rest of the windpipe and the gullet, leaving that for someone else.
"U'meirek acher shechitah al yado" - another person completed the slaughter for him, after he had already performed the measure that renders it valid. And the reason for this: he needed to perform the next act immediately - "kibel es hadam", to receive the blood into a vessel, "u'zerako", and to throw the blood on the altar. In order to be able to do this with the required speed, he needed another person to complete the slaughter for him.
The services in the Heichal:
"Nichnas l'haktir ketores shel shachar" - he entered the Heichal, into the Sanctuary, to burn the morning incense on the inner golden altar.
"L'heitiv es haneiros" - to clean the lamps of the Menorah and prepare them for that evening.
Completing the tamid offering:
"L'hakriv es harosh v'es ha'ever" - the head of the tamid animal and the accompanying limbs, all of which were burned completely, since it is an olah offering.
"V'es hachavitin" - the chavitin meal offering that the Kohen Gadol brought every single day of the year.
"V'es hayayin" - the wine that was poured out on the altar.
It is worth noting that the Mishnah does not mention the minchah, the fine flour offering that accompanied the tamid, but it is considered included together with the other components.
In summary: In this Mishnah we learned the order of the first immersion - the spreading of the linen sheet as a partition, a reminder of the linen garments of that day; the removal of his personal clothing, the immersion, the drying, the donning of the golden garments and the sanctification of the hands and feet. We then examined the service of the tamid: the initial slaughter that another completed on his behalf, so that he could receive the blood and throw it immediately; the burning of the morning incense and the cleaning of the lamps in the Heichal; and the completion of the offering with the bringing of the head and the limbs, the chavitin and the wine.