Megillah, Chapter 3, Mishnah 5. This Mishnah lists the various Torah readings we read on the festivals, and from it we will also note the difference between the Mishnah's ruling and the practice we follow today.
On Pesach:
"BaPesach korin b'parashas mo'ados shel Toras Kohanim" - we read the portion of the festivals in Toras Kohanim, that is, the portion of the festivals in the book of Vayikra, in Parashas Emor.
In practice, however, our custom today is different:
On the first day: "Mishchu u'kchu" from Parashas Bo.
On the second day: the portion of the festivals in Toras Kohanim, as the Mishnah rules here.
On the seventh day: Parashas Beshalach, since this is the day on which the splitting of the sea took place.
On the eighth day: "Kol habechor" in Parashas Re'eh, as is read on every final day of a festival.
On Atzeres:
On Shavuos we read "Shivah shavuos" - from Parashas Re'eh, from the section of the festivals there, which deals with the festival of Shavuos. Here too our custom today is different: on the first day of Shavuos we read about the giving of the Torah, in Parashas Yisro, in the Ten Commandments; and on the second day we read "Kol habechor" in Parashas Re'eh, which includes within it the passage of "Shivah shavuos."
On Rosh Hashanah:
We read "BaChodesh hashevi'i b'echad lachodesh" - the passage dealing with Rosh Hashanah, which is also in Parashas Emor in the book of Vayikra. In practice, however, on the two days of Rosh Hashanah we do as follows: on the first day we read the passage of Sarah, who was remembered by Hashem, and the birth of Yitzchak, and on the second day we read the passage of the Akeidah, the binding of Yitzchak.
On Yom Kippur:
We read "Acharei mos" - the passage of the Yom Kippur service, and this is indeed our practice.
On Sukkos:
"B'yom tov harishon shel chag korin b'parashas mo'ados sheb'Toras Kohanim" - on the first day of Sukkos we read the portion of the festivals in Toras Kohanim, that is, Parashas Emor, and this is our practice on the first two days of the festival. "U'vishar kol yemei hechag b'korbenos hechag" - on the remaining days of Sukkos we read the offerings of the festival in Parashas Pinchas, which are the musaf offerings brought on those days.
The conclusion of the festival of Sukkos is Shemini Atzeres, which our Mishnah did not address: on it we read "Kol habechor" in Parashas Re'eh, and on Simchas Torah we read "V'zos haberachah."