Pesachim, Chapter Ten, Mishnah Two. This mishnah presents a dispute between Beis Shammai and Beis Hillel that was already taught in Maseches Berachos. The wording of the mishnah: "Mazgu lo kos rishon" - they pour for a person the first cup of wine at the Seder, and from the phrase "they pour for him" it emerges that it is fitting for someone else to pour the four cups for him.
The dispute between Beis Shammai and Beis Hillel regarding the order of the Kiddush berachos:
"Beis Shammai omrim: mevarech al hayom v'achar kach mevarech al hayayin" - first the berachah of the day, 'mekadesh Yisrael v'hazmanim', and after it the berachah of 'borei pri hagafen'.
"U'Beis Hillel omrim: mevarech al hayayin v'achar kach mevarech al hayom" - first the berachah of 'borei pri hagafen', and after it the berachah of Kiddush, 'mekadesh Yisrael v'hazmanim'.
The reasons for the dispute, as explained in the beraisa:
The reason of Beis Shammai: the day is what causes there to be an obligation of wine at all, and therefore the berachah on the day comes first, and only after it the berachah on the wine.
The reason of Beis Hillel: the wine is what causes the berachah of Kiddush to be recited, and therefore the berachah on the wine should come first. Furthermore, the berachah on wine is more frequent, and there is a principle that 'when one item is frequent and another is not frequent, the frequent one comes first': the more common berachah is recited first, and therefore we say 'borei pri hagafen' at the outset.
The halachah is decided like Beis Hillel, and that is our practice.
In summary: in this mishnah we learned the order of the berachos over the first cup: according to Beis Shammai the berachah of the day comes first, since the day is what brings about the obligation of wine; and according to Beis Hillel the berachah on the wine comes first, both because the wine brings about the recitation of Kiddush and because it is the more frequent - and the halachah follows them.