Wearing the tzitzit (plural: tzitzyot) is also commanded in , which says: "You shall make yourself twisted threads, on the four corners of your garment with which you cover yourself."
Tzitzyot are attached today only to Jewish religious garments, such as a tallit gadol ("large prayer shawl"). This is because today's clothes do not have four corners, and thus the fringes are not necessary. Traditional Jewish men wear a tallit katan ("small prayer shawl") constantly in order to fulfill this commandment at their own volition, and some consider it a transgression to miss a commandment that one has the ability to fulfill. The tallit katan is also commonly referred to as "tzitzit," though this name technically refers to each of the fringes only.
Various reasons are given for the commandment. The Torah itself states: "So that you will remember to do the commandments". In addition, it serves as a reminder of the Exodus from Egypt (Numbers 15:40). The Talmud equates its observance with that of all the mitzvot. Rambam (Comm. Pirkei Avot 2:1) includes it as a major mitzvah along with brit milah ("circumcision") and the korban pesah ("Paschal lamb").
Though many methods exist, the one that gained the widest acceptance can be described as follows:
The four strands of the tzitzit are passed through holes near the four corners of the garment (Shulchan Aruch Orach Chaim 11:9-11,15) that are farthest apart (10:1). Four tzitzyot are passed through each hole (11:12-13), and the two groups of four ends are double-knotted to each other at the edge of the garment near the hole (11:14,15). One of the tzitzit is made longer than the others (11:4); the long end of that one is wound around the other seven ends and double-knotted; this is done repeatedly so as to make a total of five double knots separated by four sections of winding, with a total length of at least four inches, leaving free-hanging ends that are twice that long (11:14).
Before tying begins, a Hebrew blessing is said (it's more of a "declaration of intent"): L'Shem Mitzvat Tzitzit ("for the sake of the commandment of tzitzit"). Some rabbis are of the opinion that one should instead say a full blessing: Baruch atah Adonai Elohainu Melech HaOlam, asher kiddishanu b'mitzvotav v'tzivanu la'asot tzitzit ("Blessed are you, Lord, our God, King of the universe who sanctified us with His commandments and commanded us to make [the] tzitzit.)
The two sets of stands are knotted together twice, and then the shamash (a longer strand) is wound around the remaining seven strands a number of times (see below). The two sets are then knotted again twice. This procedure is repeated three times, such that there are a total of five knots, the four intervening spaces being taken up by windings numbering 7-8-11-13, respectively. The total number of winds comes to 39, which is the same number of winds if one were to tie according to the Talmud's instruction of 13 hulyot of 3 winds each. Furthermore, the number 39 is found to be significant in that it is the gematria (numerical equivalent) of the words: "The Lord is One" Deuteronomy 6:4). Others, especially Sephardi Jews, use 10-5-6-5 as the number of windings, a combination that represents directly the spelling of the Tetragrammaton (one of God's names).
Rashi, a prominent Jewish commentator, bases the number of knots on a gematria: the word tzitzit (in its Mishnaic spelling) has the value 600. Each tassel has eight threads (when doubled over) and five sets of knots, totalling 13. The sum of all numbers is 613, traditionally the number of mitzvot (commandments) in the Torah. This reflects the concept that donning a garment with tzitzyot reminds its wearer of all Torah commandments.
Nachmanides disagrees with Rashi, pointing out that the Biblical spelling of the word tzitzit has only one yod rather than two, thus adding up to the total number of 603 rather than 613. He points out that in the Biblical quote "you shall see it and remember them", the singular form "it" can refer only to the "p'til" ("thread") of tekhelet. The tekhelet strand serves this purpose, explains the Talmud, for the blue color of tekhelet resembles the ocean, which in turn resembles the sky, which in turn is said to resemble God's holy throne - thus reminding all of the divine mission to fulfill His commandments.
Tekhelet (תכלת) is color dye which the Hebrew Bible commands the Jews to use for one, more or all of the fringes on Tzitzit. At some point in Jewish history, the source of the dye was lost and since then, Jews have worn plain white tzitzyot without any dyes. Tekhelet, which appears 48 times in the Tanakh - translated by the Septuagint as iakinthos (blue) - is a specific blue dye produced from a creature referred to as a chilazon, other blue dyes being unacceptable (Tosefta). Some explain the black stripes found on many traditional prayer shawls as representing the loss of this dye.
Karaites wear tzitzyot with blue threads in them. In contrast to Rabbinic Judaism, they believe that the tekhelet (the "blue"), does not refer to a specific dye. The traditions of Rabbinic Judaism used in the knotting of the tzitzit are not followed, so the appearance of Karaite tzitzit can be quite different from that of Rabbanite tzitzit. Contrary to some claims, Karaites do not hang tzitzyot on their walls.
Rainbow tzitzit are tzitzit with multi-colored strings. There are many opinions in the Halakha as to what color the strings of the tzitzit should be. The Shulchan Aruch (Orach Chaim 9:5) records a view requiring that the garment and Tzitzit be the same color, and recommends abiding by this stringency. The Mishna Berura explains that the reason for this is either to beautify the mitzvah, or because the tzitzit must be similar to the garment. The Rama (ad loc) says that the minhag of Ashkenazim is not to wear colored tzitzit, and that one should abide by that minhag. Some people around the world have started wearing rainbow-colored tzitzit, but the validity of using colored strings (aside from tekhelet)is very questionable because colors may only be used if the garment is the color of the strings.