Before us is Mishnah 3 in the second chapter of Maseches Nazir. The Mishnah opens: "Mazgu lo kos ve'amar hareini nazir mimenu - harei zeh nazir" - if they poured him a cup of wine, and after it was poured he said that he is a nazir from it, his vow takes effect and he is a nazir in every respect.
This principle was already taught in the first chapter, in Mishnah 2: one who says that he is a nazir from the chartzanim - the seeds of the grapes - has taken a valid vow of nezirus, even though he mentioned only one detail out of all the nazir's prohibitions, since that detail is among the things the Torah forbade to him. So too here: since he attached his nezirus to the cup of wine that was poured before him, his nezirus stands, and all the laws of nezirus apply to him.
The Added Words in the Mishnah's Wording:
The Mishnah goes on to relate an incident that occurred, but in order to understand how the incident fits with the law stated at the beginning of the Mishnah, the Gemara explains that words are missing here, and the Mishnah must be read with an additional teaching. This is how it reads:
"Mazgu lo kos ve'amar hareini nazir mimenu" - he is a nazir, as explained above.
"Ve'im hayah shikor ve'amar hareini nazir mimenu" - he is not a nazir. The meaning of his words is not an acceptance of nezirus, but rather that he does not wish to drink any more wine because he is drunk. There is no intention here of a general nezirus, only a refusal to drink the cup in front of him.
The Incident in the Mishnah:
This law rests on the incident brought further on: "Ma'aseh be'ishah achas shehaysah shikorah, umazgu lah kos ve'amrah hareini nezirah mimenu" - there was an incident with a certain woman who was drunk, and they poured her a cup and she said, "I am a nezirah from it." That woman had drunk more than was fitting, yet she was still of clear mind, and in the midst of her drunkenness they poured her another cup, and she said that she was a nezirah from it.
The Sages said about this incident - based on the context in which the words were spoken - "shelo niskavnah ela lomar harei alai korban" - that she intended only to say, "This is forbidden to me like a korban." In other words, her entire intention was to forbid herself from benefiting from that cup alone, and not to accept upon herself a general nezirus.
In summary: In this Mishnah we learned that one who says "I am a nazir from it" about a cup of wine that was poured before him has a valid nezirus, following the rule of one who mentions a single detail of the nazir's prohibitions; however, if a drunken person said this, his words are not an acceptance of nezirus but a refusal to drink that particular cup, and this is borne out by the Sages' ruling in the case of that drunken woman, who intended only to forbid herself the cup in front of her.