Gemara

(Rava): There are 30 days from Purim until Pesach, during which we teach the laws of Pesach.

(Beraisa): We ask Hilchos Pesach 30 days before Pesach;

R. Shimon ben Gamliel says, we ask two weeks beforehand.

Bechoros 57b (Mishnah - R. Akiva): There are three Granos (times for tithing animals): Pras Pesach, Pras Shevuos, and Pras Sukos.

Ben Azai says, the times are Adar 29, Sivan 1, and Av 29.

58a (R. Avahu): 'Pras' means half (of the time (30 days) before Pesach during which Halachos of Pesach are learned).

Pesachim 6a: Chachamim's learn from "v'Ya'asu... Es ha'Posach b'Mo'ado ...; Va'Yhi Anashim Asher Hayu Temei'im..." (on Pesach Rishon, Moshe exhorted Benei Yisrael about Pesach Sheni a month later) R. Shimon ben Gamliel learns from "be'Asor la'Chodesh ha'Zeh va'Yikchu Lahem Ish Seh..." (on Nisan 1, Moshe exhorted Benei Yisrael about Pesach Rishon on the 14th).

Avodah Zarah 5b - Question: Three days do not suffice to prepare a Korban! We start teaching laws of Pesach 30 days or two weeks before!

Answer: Even tiny blemishes disqualify a Korban for a Yisrael. A Nochri may offer any animal not missing a limb, so three days suffices for him.

Megilah 4a (R. Yehoshua ben Levi): When Purim falls on Shabbos, we ask and expound about the day.

Question: This is obvious. The same applies to any Yom Tov!

(Beraisa): Moshe enacted that we expound Hilchos Pesach, Shevuos and Sukos, each on its day!

Answer: Rabah taught that the decree not to read the Megilah on Shabbos was lest one carry a Megilah in a Reshus ha'Rabim.) R. Yehoshua ben Levi teaches that we expound it on Shabbos, without concern lest one carry it.

29b - Suggestion: (Mishnayos teach that we read Parashas Shekalim before Rosh Chodesh Adar.) These are unlike R. Shimon ben Gamliel (who says that we begin learning Hilchos Pesach only two weeks before)!

Rejection: They can even be like R. Shimon ben Gamliel. We read two weeks before we set up moneychangers' tables for Shekalim.

Berachos 17b (Rav Ashi): People in Masa Machsiya see the honor of Torah twice every year (Chachamim gather to learn the laws of the festival).

Bava Metzia 86a: Someone informed on Rabah that he causes thousands of Yisre'elim to avoid taxes (because they gather to learn from him) for a month in spring and a month in fall.

Rishonim

Rif (Pesachim 2b): We ask Hilchos Pesach 30 days beforehand.

Question: The Beraisa in Megilah connotes that we expound about the festival only on the festival (but not before)!

Answer #1 (Ran DH ha'Oseh): It is not an obligation to ask about laws of Pesach 30 days (or two weeks) before Pesach. Rather, normally, if one Talmid asks k'Inyan (about what is being learned), and the other asks Lo k'Inyan, we answer (first) the one who asked about k'Inyan. A question about Pesach within the 30 days before is considered k'Inyan.

Answer #2 (Beis Yosef OC 429 DH Tanya): We must inform people about laws of Pesach 30 days in advance so they will have time to grind the wheat, bake the Matzah, Kasher Kelim and destroy Chametz. It does not help to teach about these during Pesach if they were not done properly beforehand! This does not apply to Shavuos, which has no special laws unlike a regular Yom Tov. Sukos has special laws, but they do not require so much learning. Even the Sukah of a Nochri or woman... is Kosher! Most Lulavim and Esrogim are Kosher. Also, the toil for Sukah and Lulav is not so great. One can do them on Erev Yom Tov. We ask about and expound the Halachos of each festival on that festival, i.e. the reasons why Hash-m commanded this festival, and laws of Yom Tov. Surely we must say so about Shavuos, which has no special Halachos! Teaching the Halachos beforehand is 30 days before Pesach, and a day or two before Sukos. In Avodah Zarah we say that 30 days are needed due to the Korban, so everyone will have time to get an animal and check it for blemishes. Even though this does not apply nowadays, we keep the enactment.

NOTE: If 30 days is for the Korban, this should apply to every festival, for every man must offer at least two Korbanos! Perhaps Pesach is different, for one must have a share of a Kosher Korban on Erev Pesach. For other festivals, if one brought an animal with a blemish, Kohanim would tell him, and he would have six or seven days from the first day to find and offer a Kosher Korban! Also, one who does not bring Pesach is Chayav Kares.

Answer #3 (Taz 429:1): There are monetary consequences of the 30 days of asking. Rava taught that Talmidim are considered to be working for the Rebbi, for he can decide to learn a particular tractate lest he forget it, and they cannot refuse. (Therefore, if he borrows an item from them, he is exempt for any loss - Bava Metzia 97a.) The Gemara says that when we learn Hilchos ha'Chag before the Chag, he is working for them.

Rashi (Sukah 9a DH Beis Shamai): Beis Hillel admit that a Sukah made within 30 days of Sukos is Kosher, for then we ask about Hilchos ha'Chag, and presumably it was l'Shem Sukah.

Tosfos (Megilah 4a DH Mai): The Gemara asked, since we expound Hilchos Yom Tov on Yom Tov, even though we learn them from 30 days before Yom Tov, we need not teach that we expound Hilchos Purim on Purim, since we do not learn them beforehand!

Tosfos (Bechoros 57b DH bi'Fros): The main reason we expound 30 days before the festival is due to the Korbanos, like it says in Avodah Zarah. Also the source for 30 days or two weeks was based on Korbanos. If so, we should start learning 30 days before Erev Pesach! It seems that Chachamim did not distinguish, and always count back from the primary day of Yom Tov.

Poskim

Shulchan Aruch (OC 429:1): We ask about laws of Pesach 30 days before Pesach.

Magen Avraham (1): The Bach and Maharsha say that we learn the Halachos of every Yom Tov 30 days beforehand. Bechoros 58a proves this. Megilah 4a connotes that there is a Chiyuv to expound the matters of each Yom Tov on its day, e.g. Yetzi'as Mitzrayim on Pesach.

Gra (1): Even though Avodah Zarah discusses Pesach, the same applies to other festivals, on which everyone offers Chagigah. Megilah 29b proves that 30 days applies to all festivals. We begin from Purim. We do not need 30 days before Shavuos, like it says in Berachos and Bava Metzia. This is like the opinion in Bechoros that the Goren before Shavuos is Sivan 1, since few animals were born (after the previous Goren, so we delay it). We should start learning from then. Megilah 29 holds that we expound before each festival; the Tana'im in Bechoros argue about the time needed for Shavuos. The Yerushalmi says that we learn for 30 days before all three festivals. This is like the first Tana.

Mishnah Berurah (1): The same applies to every Yom Tov. The Gra holds that for Shavuos, it suffices to start from Sivan 1. Some say that Pesach requires 30 days, but some days suffice for other Yomim Tovim. All agree that on Yom Tov itself we must expound the laws of that Yom Tov.

Mishnah Berurah (2): Nowadays we expound on Shabbos ha'Gadol (if Erev Pesach is Shabbos, the Shabbos before this) and Shabbos Shuvah. The primary reason is to teach practical Halachah - Kashering, getting rid of Chametz, baking Matzos and other Hilchos Pesach, and on Shabbos Shuvah, laws of Yom Kipur and Sukos, in addition to Teshuvah. One is not Yotzei through a Drashah of mere Pilpul or Drush (rhetoric or ideas not relevant to Halachah). In any case it is a Mitzvah for everyone to engage in Hilchos Pesach 30 days beforehand, and also on the festival itself.

Kaf ha'Chayim (4): R. Zalman says that nowadays that all Halachos are written, on Yom Tov itself we expound Agada about the day.

Kaf ha'Chayim (3): In some places they expound about every Mo'ed on the Shabbos before, including Rosh Hashanah, Yom Kipur and Shavuos. The primary enactment was to begin with Agada and Musar to appeal to people, and to conclude with practical Halachah. I do so.