Gemara

31b (Mishnah): If one accepted Nezirus and he asked a Chacham to permit it, but the Chacham did not, he counts his Nezirus from the day he vowed (even if he was not observing the laws of Nezirus).

Question: Our Mishnah is not like R. Yosi, nor like Chachamim!

(Beraisa): If one transgressed his Nezirus, we do not deal with him (permit his vow) until he observes the Isur for as many days as he transgressed;

R. Yosi says, it suffices to observe the Isur for 30 days.

Our Mishnah is unlike Chachamim, who obligate observing extra days when he accepted a short Nezirus (and the same applies to a long Nezirus)! It is unlike R. Yosi, who says that 30 days suffices, even if he accepted a long Nezirus! (The Mishnah obligates completing the term that he accepted.)

Answer #1: The Mishnah is like R. Yosi. It discusses only a short Nezirus.

Answer #2: The Mishnah is like Chachamim. Do not read 'he counts Nezirus from the day he accepted', rather, he counts (extra) days like from the day he accepted (and transgressed).

Nedarim 20a (R. Yosef): Since the Beraisa says that we don't permit him (before he observes the Isur), a Beis Din that did so acted improperly.

(Rav Acha bar Yakov): We excommunicate the Beis Din.

Rishonim

The Rif (Nedarim 6b) brings the Beraisa, Rav Yosef and Rav Acha.

Rambam (13): If one vowed to be a Nazir and did not think that it is a vow, and acted as if it is permitted he drank wine, and afterwards a Chacham told him that it is a vow, he counts from when he vowed. Mid'Rabanan, he must observe (additional) days of Isur equal to the days he acted as if it is permitted.

Radvaz: 'We do not deal with him until (he observes days of Isur...) connotes that this is only mid'Rabanan. Mid'Oraisa he counts from when he vowed, like the simple reading of the Mishnah. This is like Ones, for he did not know that he is forbidden.

Rambam (14): E.g. if he vowed for 30 days and did not observe it for 10 days, and observed 20 days, and after 30 days a Chacham forbade to him, he counts 10 days corresponding to the 10 days he did not observe.

Radvaz: The Rambam teaches that even if he asked after finishing Nezirus, he must observe corresponding to the days he acted as if it is permitted. We do not say 'what was, was.'

Rambam (ibid.): If he shaved, drank, or become Tamei during these 10 days, he is lashed mid'Rabanan.

Rashbash (610 DH uv'Perek 4): The Gemara did not discuss a punishment for one who transgresses during the extra days he must observe corresponding to the days he transgressed. The Rambam obligates lashes mid'Rabanan because he is commanded mid'Rabanan.

Rambam (15): This refers to a short Nezirus. If he accepted a long Nezirus, it suffices to conduct 30 days of Nezirus, even if he transgressed all days of his long Nezirus. We do not deal with one who did not observe the Isurim by himself.

Ra'avad: This means that if he asks us to permit it, we do not.

Rambam (16): If a Beis Din permits him or someone similar, and tells people who disgrace Nedarim that the Torah does not obligate them, or instructs them to be lenient, or is Pose'ach (suggests why the vow was mistaken), we excommunicate this amateur Beis Din.

Rosh (Nedarim 2:11): R. Yosi says that 30 days suffices only for Nezirus, for Stam Nezirus is 30 days. He agrees that one who transgressed other vows must conduct Isur as many days as he transgressed.

Ramban (Mishpat ha'Cherem, brought in Beis Yosef YD 208 DH Kosav ha'Rashba): The Ra'avad says that 30 days suffice only for Nezirus, but one who transgressed other vows must conduct Isur as many days as he transgressed. Others disagree, for we are not more stringent about Nedarim, for which no Korban is brought, than for Nezirus, for which a Korban is brought (for transgressing Tum'ah). This seems correct. The Gemara in Nedarim brought the Beraisa about Nezirus because the law is the same.

Rosh (ibid.): A case occurred in which one forbade to himself all produce other than grain and transgressed many days. They permitted him immediately, without conducting Isur first, for he would have transgressed again; he could not be careful about this. Since it is only a fine, we are not stringent when he cannot be careful.

Ran (Nedarim 20a DH ul'Inyan): Also, he was permitted immediately lest he get weak and be unable to serve Hash-m properly. The Chacham was stringent to permit only through a Pesach, not with mere regret.

Poskim

Shulchan Aruch (YD 208:2): If one took a proper vow mid'Oraisa and (Rema - intentionally) transgressed it, we fine him and do not permit him unless he observes it for as many days as he transgressed. If he might stumble, e.g. he vowed about something that he cannot be careful about, e.g. not to eat any produce other than grain, and transgressed it, we permit him immediately. We do not fine him to conduct Isur first, lest he transgress. Some say that in any case we are stringent and do not permit him through regret; we require a Pesach.

Shulchan Aruch (ibid.): From here we learn that if one forbade to himself meat and wine if he will transgress a certain Isur, and he transgressed it and ate meat or wine, we permit him immediately, lest he transgress again.

Shach (12): If he asks to permit it in order to transgress, some say that we do not permit him.

Rema: If the Chacham thinks that the Noder can be careful about the Isur, we do not permit him until he conducts Isur as many days as he transgressed.

Shulchan Aruch (3): He must observe the Isur for as many days as he transgressed, if this is a small amount. If it is a lot, 30 days suffices.

Beis Yosef (DH Kosav ha'Rashba (5:258)): The Rashba rules like R. Yosi. The Rambam rules like R. Yosi regarding Nezirus. He did not mention Nedarim. Presumably, Nedarim are like Nezirus.

Gra (4): The Halachah follows R. Yosi against R. Yehudah. (In Nedarim 20a, the first Tana is R. Yehudah.) In a Tosefta (Nedarim 1:11) R. Yosi and R. Yehudah argue about Nedarim. The Tur rules like R. Yehudah because his opinion is brought Stam and is called 'Rabanan' in Maseches Nazir.

Beis Yosef (DH uvi'Teshuvas): We hold like all the Rabanan who say that 30 days suffice.

Rebuttal (Shach 13): Tosfos (20a DH Aval Nezirus), the Rosh, R. Yerucham, the Ra'avad and Rivash (395) all hold that 30 days does not suffice. It seems that the Tur agrees; the Prishah (6) understood differently. One should not be lenient.