If one hears a child recite a Beracha, does he answer "Amen"?
Two conditions must be met for a child’s Beracha to warrant a response of "Amen." First, the child must be at least six years old. The Shulhan Aruch, in the laws of Zimun (Orah Haim 199:6), writes that one responds to a child’s Beracha only if he has reached the age of "Pe’utot," which the commentaries interpret to mean six years old. If a child is below the age of six, then even if he is very advanced and mature, one does not respond to his Beracha.
The second condition is that the child understands that he recites the Beracha to Hashem. If a parent has a child recite a Beracha so he grows accustomed to doing so, but the child does not understand the concept of reciting a Beracha to God, then one does not answer "Amen" to that child’s Beracha.
This is the ruling of Hacham Ovadia Yosef, in his work Yabia Omer (vol. 2, Orah Haim 13:11).
Rabbi Moshe Halevi (Israel, 1961-2001) also codifies this Halacha, in his work Birkat Hashem (vol. 1, 6:10; listen to audio recording for precise citation), adding that one certainly should not respond "Amen" if a child recites a Beracha in a situation that does not require a Beracha. Meaning, if a child recites the words of the Beracha because he is being taught the text, but he is not eating anything or performing any activity that warrants the recitation of a Beracha, then one should not respond "Amen." It is only when a child recites a Beracha in a situation where it is warranted – like before eating – that one should respond "Amen" if the two aforementioned conditions are met.
Rabbi Moshe Halevi adds (in a footnote) that one may answer "Amen" to a child’s Beracha even if there is reason to suspect that the child’s body is unclean. Halacha forbids reciting a Beracha if one’s body is unclean, and one might have therefore assumed that in the case of a child, who may not have cleaned himself properly after using the restroom, one should not answer "Amen" to his Beracha. In truth, however, one answers "Amen" even if there is reason for such a suspicion, since "Be’di’abad" (after the fact) the child’s Beracha is valid even if it was recited with filth on the body.
Summary: If a child recites a Beracha, such as before eating, one who hears the Beracha answers "Amen" only if the child is at least six years of age, and the child understands that the Beracha is recited to Hashem. One may answer "Amen" in this case even if he has reason to suspect that the child’s body is unclean.