Sukkah, Chapter 4, Mishnah 10. The Mishnah continues clarifying how the mitzvah of the water libation was carried out, and teaches the way it was performed on Shabbos.
The libation on Shabbos:
The Mishnah states: "Kema'asehu bachol kach ma'asehu baShabbos" - the entire procedure of the libation was the same on Shabbos as it was on weekdays, with one exception: from Erev Shabbos they would fill "chavis shel zahav she'einah mekudeshes" - a golden barrel that was not sanctified - from the Shiloach, from that very same spring. Although the barrel was made of gold, it did not have the status of a kli shareis, a vessel used in the service of the Beis HaMikdash.
Why specifically in a vessel that is not sanctified:
Anything designated to be offered on the altar becomes sanctified the moment it is placed into a kli shareis - and from that point on, if it remains overnight it becomes disqualified, and this disqualification is called linah. For this reason they would place the water in a vessel that had no sanctity and leave it in one of the chambers, and the next day they would transfer it into a kli shareis, which sanctified it.
"Nishpechah o nisgalsah":
If the water spilled, or if it was left uncovered - in the times of the Mishnah and the Gemara there was a concern that a snake had injected venom into it, and since it was no longer fit for drinking it was likewise no longer valid for use on the altar. On Shabbos it was impossible to go out and draw water from the Shiloach, and therefore "hayah memalei min hakiyor" - he would fill it from within the Beis HaMikdash itself, from the Laver from which the kohanim sanctify their hands and their feet.
It is a general rule that wine or water designated to be offered on the altar which was left uncovered becomes disqualified for use on the altar, since it is no longer fit for a person to eat or drink.
Why specifically from the Shiloach:
The Gemara notes that the source for this is a verse, from which we learn that the water for the libation is drawn from a spring; therefore they would take it from the Shiloach whenever this was possible. Nevertheless, this is not indispensable, and the mitzvah is fulfilled even with water drawn from the Laver.
In summary: In this Mishnah we learned that the procedure of the water libation on Shabbos was identical to the weekday procedure, except for the filling done while it was still day in a golden barrel that was not sanctified - in order to avoid the disqualification of linah, which would have applied had the water been placed into a kli shareis. We saw the concern regarding water that spilled or was left uncovered, which is unfit for the altar just as it is unfit for a person, and the solution of filling from the Laver inside the Beis HaMikdash; and we also saw the preference for drawing from the Shiloach, derived from the verse, which is not indispensable to the fulfillment of the mitzvah.