Gemara

42b - Mishnah: If the seventh day of Sukos is Shabbos, the Aravah is taken (by itself, in the Mikdash) all seven days. If not, it is taken six days, but not on Shabbos.

43b - R. Yochanan: It is Docheh Shabbos to publicize that it is mid'Oraisa.

Question: If so, it should always be Docheh Shabbos!

Answer: If so, people would say that it is mid'Oraisa but Lulav is not (for in the Mikdash Lulav is Docheh Shabbos only on the first day).

Question: Also nowadays (after the Churban, we take the Aravah on the seventh day to commemorate taking it in the Mikdash), Aravah should be Docheh Shabbos!

Answer: We (in Chutz la'Aretz) have a doubt which is the seventh day.

Question: They (in Eretz Yisrael) have no doubt. For them, it should be Docheh Shabbos!

Answer #1 (Bar Hedya): (Even before the calendar was fixed, we ensure that) the seventh day never occurs on Shabbos (Beis Din can decide to make month short or long (29 or 30 days) whether or not the moon was seen).

Objection: Ravin and all those who came from Eretz Yisrael said that the seventh day sometimes occurs on Shabbos, and Aravah does not Docheh Shabbos!

Answer #2 (Rav Yosef): Perhaps in the Mikdash the Aravah was not taken in the hand, rather, it was stood up against the Mizbe'ach. (Since our commemoration is unlike Aravah it in the Mikdash, it is not Docheh Shabbos.)

Rejection (Beraisa): A case occurred, Aravos were prepared in the Mikdash for the seventh day, which was on Shabbos. Baisusim hid the Aravos, for they (reject Torah she'Ba'al Peh and) say that Chivut Aravah (waving or banging it) is not Docheh Shabbos. (This shows that we take the Aravah in the hand!)

Answer #3: Since the Aravah is not Docheh Shabbos in Chutz la'Aretz, it is not Docheh even in Eretz Yisrael.

44a - Question (Abaye): Nowadays, why do we take the Lulav all seven days (except for Shabbos) to commemorate the Mikdash, but we take the Aravah only on the seventh day?

Answer (Rava): We are Yotzei Aravah every day with the Aravos with the Lulav.

Question: The Aravos with the Lulav are solely for the sake of the Mitzvah of the four Minim!

Suggestion: Perhaps we take the Lulav bundle (with Aravos) a second time for the sake of Aravah!

Rejection: This is not the practice.

Answer: Rava taught that since Lulav is mid'Oraisa, we take it all seven days to commemorate the Mikdash. Aravah is mid'Rabanan, so we do not take it all seven days.

Objection: This is unlike Aba Sha'ul, who says that "Arvei" alludes to two Aravos, one with the Lulav, and one taken in the Mikdash. It is also unlike Chachamim, who have a tradition from Sinai for Aravah in the Mikdash!

Correction: Rather, since there is a source in (written) Torah for Lulav, we take it all seven days. Aravah has no source in Torah, so we do not take it all seven days.

R. Yochanan: Nevi'im enacted to take the Aravah.

R. Yehoshua ben Levi: It is a custom initiated by Nevi'im.

Question: But R. Yochanan said that it is a tradition from Moshe from Sinai!

Answer #1 (R. Avahu): It was forgotten, and Nevi'im re-established it.

Objection: R. Yochanan said that Torah was not forgotten in Bavel!

Answer #2: It is a tradition from Sinai in the Mikdash. Nevi'im enacted to take it outside the Mikdash.

R. Ami: There is a Shi'ur to Aravah. It must be taken by itself; one is not Yotzei with the Aravah with the Lulav.

The repetition teaches that even if he took the Lulav bundle again l'Shem Aravah, he was Yotzei.

Rav Chisda: One is Yotzei with the Aravah with the Lulav.

Rav Nachman: Three branches with moist leaves are required.

Rav Sheshes: Even one branch with one leaf suffices.

Aravos were brought in front of R. Eliezer b'Rebbi Tzadok and Rav. They took them, did Chavatah twice, and did not bless. They hold that it is a custom of the Nevi'im.

Rishonim

Rif: We conclude that Aravah is a custom initiated by Nevi'im, therefore we do not bless on it. Amora'im argue about whether or not one is Yotzei with the Aravah in the Lulav, and whether we require three branches with moist leaves, or only one branch with one leaf.

Ran (DH v'Kamah): Since it is a custom of Nevi'im, we are lenient like Rav Sheshes (one branch suffices).

Rambam (Hilchos Lulav 7:20): A tradition from Sinai teaches that we take the Aravah in the Mikdash aside from the Aravah with the Lulav. One is not Yotzei with the Aravah with the Lulav. Even one branch with one leaf suffices.

Rambam (22): Since the Aravah is not explicit in the Torah, nowadays we do not take it all seven days to commemorate the Mikdash, rather, only on the seventh day. We take one branch or many, apart from the Aravah with the Lulav. We bang it on the ground or on a Keli two or three times without a Berachah, since it is a custom of the Nevi'im.

Griz (Al Rambam Hilchos Berachos 11:16): Rashi says that we cannot bless 'v'Tzivanu' on a custom. The Rambam holds that we are commanded to follow customs established by Chachamim! Rather, we bless only if the initial enactment was to do a Mitzvah. Tosfos says that we do not bless on the custom of Aravah, for it is mere movement, but we bless on Hallel even when it is a custom, it is important, like Kri'as ha'Torah. This is because customs are not important enough to warrant Berachos, unless the custom itself is an important matter.

Rosh (4:1): We conclude that Aravah is a custom of initiated by Nevi'im. This is why R. Eliezer b'Rebbi Tzadok took an Aravah and did not bless. He holds that it is a custom of the Nevi'im. R. Shmuel bar Chofni says that the Halachah follows R. Yochanan against R. Yehoshua ben Levi. People conduct like the Rif; since Rav and R. Eliezer b'Rebbi Tzadok did not bless in practice, we follow them. The Ge'onim always rule like R. Yehoshua ben Levi. A Gaon says that we take the Lulav in Shacharis and bang the Aravah twice during Musaf. The Aravah is taken without anything tied to it, but we are not concerned if he has something else in his hand. The Rambam rules like R. Ami, who says that one is not Yotzei with the Aravah with the Lulav, even if he picks it up again for the Aravah. Avi ha'Ezri rules like Rav Chisda, that one is Yotzei if he picks it up again for the Aravah. This is more reasonable, for Rav Chisda cited Rav Yitzchak and did not argue, so they are two against R. Ami. The Ge'onim say that the Halachah follows Rav Nachman in monetary laws, but the Halachah follows Rav Sheshes in Isurim, therefore one branch with one leaf suffices. The Rambam and Ritz Gei'us say that we bang it on the ground or on a Keli two or three times. Rashi says that 'Chavit' is shaking it.

Poskim

Shulchan Aruch (664:2): On the seventh day we take an Aravah aside from the Aravah with the Lulav. We do not bless on it.

Mishnah Berurah (12): Since it is only a custom, we cannot bless '...v'Tzivanu'.

Shulchan Aruch (4): Even one branch with one leaf suffices.

Rema: However, it is unseemly to have only one leaf on the branch. The custom is to use nice Aravos, to fulfill "Zeh Keli v'Anvehu".

Mishnah Berurah (16): L'Chatchilah there should be at least three branches. The Ari Zal says that there should be five.

Eshel Avraham (4,7): Some say not to bind Aravos with (rings made from) a Lulav, because it is a Chatzitzah. The Magen Avraham says that anything to beautify it is not a Chatzitzah. It seems that we are concerned for Chatzitzah, but not for Bal Tosif (adding to a Mitzvah). Perhaps there is no Mitzvah to bind Aravos, for one suffices. It is best to bind them with Aravah stalks (the same species is not a Chatzitzah).

Mishnah Berurah (17): Some say not to bind the Aravos. The Ramaz says that they should be bound, and this is the custom.

Shulchan Aruch (ibid.): The Aravah must be as long as the Aravah in the Lulav must be.

Source (Gra DH v'Shi'ur): We do not find that they were lenient about the length, therefore it must be like the Aravah with the Lulav (three Tefachim). Also, Aba Sha'ul learned this Aravah and the Aravah with the Lulav from the same verse.

Rema: Whatever disqualifies the Aravah with the Lulav disqualifies here.

Kaf ha'Chayim (34): The Magen Avraham says that there is one leniency: if most of the leaves fell off, it is Kosher. The Ari Zal does not allow this.

Mishnah Berurah (18): Stolen or dry Aravos are Pasul. Withered is Kosher, but l'Chatchilah one should use moist ones.

Shulchan Aruch (ibid.): We bang it on the ground or on a Keli two or three times.

Mishnah Berurah (19): The Ari Zal says to bang it on the ground five times, and afterwards on a Keli to make the leaves fall off. One need not remove all the leaves.

Kaf ha'Chayim (36,37): Based on the Zohar, it should be beaten on the dirt (not on a floor of stone, tiles or planks), to eradicate Din and lower it to dirt. The Ari Zal does not say to bang it on a Keli.

Rema: Some say that one must shake it. The custom is to shake it, then to bang it.

Shulchan Aruch (5): It is taken by itself without anything tied to it. We are not concerned if he has something else in his hand.

Shulchan Aruch (6): One is not Yotzei with the Aravah with the Lulav, even if he picks it up again for the Aravah. Some say that he is Yotzei.

Mishnah Berurah (21): All agree that if one removed the Aravah from the Lulav bundle and took it by itself, he was Yotzei.

Kaf ha'Chayim (42): The Ari Zal requires a separate Aravah, for the Aravah from the Lulav pertains to the Midah of Chesed, and the Aravah we beat pertains to Gevurah.