Gemara

Question: A Beraisa teaches that "everyone is obligated to put Tzitzis (on the corners of his four-cornered garment)." Whom does this include?

Answer: It includes a child who knows how to cover himself (in a Talis);

(Beraisa): A child who knows how to wrap himself (in a Talis) is obligated in Tzitzis.

Sukah 42a (Beraisa): A child who knows how to shake is obligated to take a Lulav. A child who knows how to wrap himself is obligated in Tzitzis. When a child knows how to guard Tefilin, his father buys Tefilin for him.

Rishonim

Rambam (Hilchos Tzitzis 3:9): Mid'Oraisa, children are exempt from Tzitzis. Mid'Rabanan, if a child who knows how to wrap himself, he is obligated in Tzitzis in order to train him in Mitzvos.

Hagahos Maimoniyos (20): The Yerushalmi says that he must also know to cast two Tzitziyos in back and two in front properly at the time of Kri'as Shma.

Mordechai (Sukah 763): If a child who knows how to wrap himself in Tzitzis, his father buys a Talis for him. The Yerushalmi says that not only he knows to wrap himself. Rather, he knows to cast two Tzitziyos in back and two in front, and hold the Tzitziyos properly at the time of Kri'as Shma.

Tosfos (Erchin 2b DH ha'Yode'a): The child must know how to wrap himself, for wrapping unlike the Yishmaelim do is not called wrapping (Mo'ed Katan 24a). R. Yom Tov Tuv Elem says that one puts one in front and one in back on the right, and similarly on the left.

Poskim

Rema (OC 10:12): Garments that people wear in Ashkenaz and Sefard, since the corners are not made to be two in front and two in back opposite each other, they are exempt from Tzitzis.

Beis Yosef (DH Yesh): Our garments have two corners near the neck, and two below. Why don't we put Tzitzis on them? For garments that go below (the belt), we can say that since we bind them, it is as if they are closed below the belt. The Maharik (149) discusses garments cut in the middle until the navel. They have corners, but they are not square. The two corners on one side are not opposite the two on the other side. They are closed in the middle, and this separates between the upper and lower corners. However, we have garments that are not closed in the middle. In Sefard, some used to round two corners to exempt them from Tzitzis. However, everyone (else) wears them with square corners, and no one objected! The Or Zaru'a's father said that only Ituf (wrapping) is obligated, but Maharik says that one may not rely on this at all. Also, we bless on a Talis Katan without Ituf! I saw in the name of R. Chasdai that only a square piece like our Taleisim is obligated. He did not explain this. I say that "Kesus" (which the Torah obligates) is only what is to protect from heat or cold. This garment is only for honor. Even one who is fully clothed is particular to wear it. Even though sometimes it warms a person, this is not its purpose. Alternatively, if we would obligate them in Tzitzis, the lower Tzitziyos would constantly snap through being trampled, and one would need to constantly fix them. The Torah did not obligate in such a case - "Deracheha Darchei No'am." Whenever the Halachah is shaky, we follow the custom.

Rebuttal (Darchei Moshe 6): These answers are wrong. Our Taleisim are only for the Mitzvah, and not to protect from heat or cold. Will you say that we bless l'Vatalah?! The Tzitziyos of Ben Tzitzis ha'Keses used to drag on the ground (Gitin 56a), and there was no concern because he needed to constantly fix them. Rather, it is because the Mitzvah is (l'Chatchilah) with two corners in front and two in back. The Roke'ach brings a Medrash (Yalkut Shimoni Beshalach 234) that at Kri'as Yam Suf, Gavriel told the water 'be careful (not to harm) those who cast a corner with Tzitzis in back of them.' Therefore, people think that the Mitzvah is only when two corners with two Tzitziyos in back, and two are in front. The only way to wear our garments is with all four corners in front. There are other garments that are exempt because the two corners in back are not opposite the two in front.

Magen Avraham (13): This Halachah was shaky among the Ge'onim (Beis Yosef and Rema), and they did not find a proper reason. Therefore, one who fears Shamayim should round a corner, like the Beis Yosef said that people do in Sefard.

Mishnah Berurah (36): The Magen Avraham held that also the Darchei Moshe's answer is weak, like the Pri Megadim says. The Pri Megadim and others agree that one should round a corner, especially nowadays that Kapotas (long jackets) are open in back. Often, the majority is open. According to the Darchei Moshe, it is obligated, for the two corners in front are opposite the two in back! Therefore, one should round one of these four corners. The garment (initially) has six corners, so it is better to round another two corners, so only three corners will remain.

Kaf ha'Chayim (23): Also Rabbeinu Zalman, the Chayei Adam, Chesed l'Alafim and Ben Ish Chai hold like the Magen Avraham.

Beis Yosef (ibid.): In these lands people wear garments open in front and open slightly on the sides. They cut the two front corners, so the two back corners extend past them. Therefore, they are mostly closed (and therefore exempt from Tzitzis). Or, we can say that they are exempt like the Maharik (149) wrote to exempt garments that are not square, because the side that has two corners, they are not opposite the other two corners.

Taz (10): Darchei Moshe brought a Medrash that shows that two Tzitziyos should be in front, and two in back. Perhaps from here stemmed the practice of some people to fold one part of the Talis very much, until it is very thin and does not cover the neck at all. They intend to have two Tzitziyos in back of them. I disapprove. If so, only the head is covered, but not the body! I say that it is better like the Tugramim (Turks) who wrap the Talis like it is around the head and body, and the arm separates in the middle of the Talis, so on each side one corner is in front and one is in back. Later I saw that Tosfos says so.

Sha'arei Teshuvah (3/13): Beis Yakov (92) says in the name of the Ari Zal that based on Kabalah, all four Tzitziyos should be in front of him at the time of Kri'as Shma. There are varying opinions about this.

Bi'ur Halachah (DH Ho'il): The Pri Megadim says that a Sardak, which is totally cut in front and is cut on the left, it is exempt according to the Darchei Moshe. However, it is improper to totally exempt it, for letter of the law does not require two Tzitziyos in front and two in back. It is only l'Chatchilah. In order to obligate it in Tzitzis, one should make two corners on the right and two on the left, and a visible majority is open. If not, there will be Mar'is Ayin (it will seem that he does improperly).

Shulchan Aruch (17:3): A child who knows how to wrap himself, his father is obligated to buy Tzitzis for him to train him.

Rema: This is only if he knows to put two Tzitziyos in front and two in back, and he knows to hold the Tzitziyos in his hand at the time of Kri'as Shma.

Levush (17): It seems that the child even blesses on the Tzitzis, to get used to it, like Chinuch in all other Mitzvos.

Magen Avraham (3): The Shulchan Aruch says that his father must buy Tzitzis for him, i.e. a Talis, to train him. This is not such a Chiyuv; see 24:1.

Bach (DH Katan): The Beraisa says that if a child knows how to shake or wrap himself, he is obligated in Lulav and Tzitzis. If he knows how to guard Tefilin, his father buys Tefilin for him. The father need not buy a Lulav or a four cornered garment for his son. The father need not buy such a garment for himself! All the more so he need not buy a Lulav, which is expensive. Rather, he and his son bless on the Lulav that the Tzibur buys in partnership. Tefilin is not expensive, so he buys Tefilin for himself and for his son, to train him. The Tur says that one must buy Tzitzis for his son because nowadays everyone is careful to buy for themselves, therefore one must buy also for his son. All Chinuch of a son is so that from when he is a minor he is used to fulfilling Mitzvos like he sees his father do. The Mordechai brings from the Yerushalmi that the father must buy a Talis for his son.

Mishnah Berurah (9): One must buy a four cornered garment and put Tzitzis on it, to train him in Mitzvos. The Pri Megadim (16) and Derech ha'Chayim say that the Talis must be big enough to wrap the head and majority of the child himself. We bless only if it is at least this Shi'ur.

Kaf ha'Chayim (12): The Shulchan Aruch connotes that if the child has a four-cornered garment, the father must buy Tzitziyos, but he need not buy a four-cornered garment for him. However, the Mordechai says that he must buy a Talis for him. In any case, the father must buy Tzitzis for every four-cornered garment that the son will wear, since he is obligated in Chinuch.

Sha'arei Teshuvah (4): Eliyahu Rabah brings from Sifrei Yere'im to clothe a child in a Talis Katan from when he knows to speak, or at least from the age of three. A Siman is "Ki ha'Adam Etz ha'Sadeh." For the first three years of a tree, its fruits are Orlah (and only afterwards we benefit from it).

Mishnah Berurah (10): When he reaches 13, he is liable like an adult. The Maharil says that the custom is that even young adults do not wrap in a Talis until they marry. A Siman is that right after "Gedilim Ta'aseh Lecha" it says "Ki Yikach Ish Ishah." This is astounding. Should one neglect the Mitzvah until he marries?!

Kaf ha'Chayim (10): Others obligate from the age of six or seven, depending on his sharpness.