The Shulhan Aruch writes that a father is obligated to train his child in the Misva of Sisit, once he reaches the age of Chinuch (education). The Poskim discuss from what age this is and conclude that a boy of nine should already wear a Tallit. If a child is mature, he should begin even earlier.
The reference here is to a Tallit Gadol, whereas the Tallit Katan is generally worn at an even younger age. This is in opposition to the custom of many Ashkenazim who do not begin to wear a Tallit Gadol until marriage. Many Poskim, including the Ya'avetz (Rav Yaakob Emden, 1697-1776, Germany), decried this practice and questioned how single men could forgo such an important Misva.
There is a nice Remez (homiletical allusion) in the Torah that fathers must train their young children in the misva of Sisit. In a different context, in Parashat Emor, the Torah employs a double language of "Emor El HaKohanim V'Amarta"-"Speak unto the children of Aaron and say to them". Why does the Pasuk say both "speak" and "say"? The Rabbis answer that it teaches that Hashem told Moshe not only to tell the Kohanim, but they should also tell their young children. Similarly, this principle can be applied to the Parasha of Sisit, in which the Torah also employs a double language of "Daber El Bene Yisrael V'Amarta Alehem"-Speak unto the children of Israel and say to them." Speak to them that they should teach their children.
Children should begin wearing a Tallit Gadol from approximately the age of nine.