The Torah discusses the laws of becoming a nazirite in Numbers 6:1-21. There are three things prohibited to a nazirite: 1) drinking or eating anything that comes from grapes; 2) cutting hair; 3) contracting impurity from a dead body. The Torah provides rules for a nazirite who became impure by having someone die on or near him. Finally the Torah describes a ritual to be performed at the end of the term of naziriteship. He or she (women also can and did become nazirites) brings an offering, then the nazirite may cut his/her hair and the hair is also burnt on the altar.
The other famous description of a nazirite in the Bible is Samson, whose mother made him a Nazirite for life. The rabbis discuss the difference between life-long nazirites such as Samson and temporary nazirites, as discussed in Numbers.
It is often debated whether or not becoming a nazirite is a positive or negative step. According to Philo, a first century Jewish philosopher from Alexandria, a nazirite is holy like a priest. Just as a priest is prohibited from contracting impurity, so too is a nazirite. Amos 2:11 also compares nazirites to priests. Josephus testifies that when a person was sick, they would vow a nazirite vow as a prayer for well-being. From the Mishnah we will see that people frequently took vows of naziriteship, as a self-sacrifice to God.
However, there were sages who looked askance at the institute of naziriteship, and called the nazirite a sinner, for the Torah mandates him to bring a sin offering. This opposition to naziriteship probably should be soon as part of the general rabbinic opposition toward asceticism. There are enough things already prohibited or mandated by the Torah. One need not take upon himself more prohibitions in order to become extra holy.
To become a nazirite, one vows a vow. Hence this tractate is found in the Mishnah immediately after tractate Nedarim.