Halakha Mazmur 34:4: Mishneh Torah, Blessings, Shulchan Shel Arba & Kitzur Shulchan Arukh

Whoever responds "Amen", must not utter it with the first or last letter clipped, or unduly hurried or drawn out, but should utter it in the way it is ordinarily pronounced. He should not raise his voice above that of the reciter of the blessing. A person who is under an obligation to recite a blessing and has not heard it recited by another may not join the hearers in responding Amen.

Birkat ha-mazon is recited with at least three adults, as it is said, “Exalt the Lord with me.²³³Ps 34:4: Gadlu la-Shem iti. Gadlu is a plural imperative, so it includes at least two; iti – “with me” adds one more, making it at least three. With three, one says in the zimmun “nivarekh she-akhalnu mishelo” – “Let us bless Him from whose food we have eaten” without mentioning God’s name. And with ten one does mention God’s name: nivarekh eloheynu– “Let us bless our God.”²³⁴B. Berakhot 49b, and so the Tur and Orah Hayim 192. And one does not say “Barekhu eloheynu” – “Bless our God,” in other words, one should not exclude himself from the group. Thus I conclude that “nivarekh” is preferable, but if someone has said “barekhu,” one doesn’t hold it against him.²³⁵B. Berakhot 50a. In other words, it is acceptable to say “barekhu.” Regardless if the number of diners is eleven or 110,000, one says, “nivarekh eloheynu she-akhalnu mishelo,” because ten is the number that includes everything and there is nothing after it, unless it is doubled [?]. If one leading a zimmun of three says, “nivarekh she-akhalnu mishelo” – “Let us bless Him from whose food we have eaten,” the other two reply as if he were beginning with “Barukh she-akhalnu mishelo uv-tuvo hayinu” –“Blessed be the One from whose food we ate and by whose goodness we live.” If one leading a zimmun of ten says, “nivarekh eloheynu she-akhalnu mishelo” – “Let us bless our God from whose food we have eaten,” the rest reply with “Barukh eloheynu she-akhalnu mishelo uv-tuvo hayinu” –“Blessed be our God from whose food we ate and by whose goodness we live.” Those outside of the table answer “Amen,” which is like the matter discussed in tractate Yoma:²³⁶B. Yoma 37a. “For the name of the Lord I proclaim; Give glory to our God!”²³⁷Dt 32:3. When “I proclaim the name ‘Lord,’ You give glory to ‘Eloheynu,’ namely, you should answer “Amen.”

You must be very careful to say the word Amein properly, and not say the Aleph hastily nor "swallow" the Nun.²²I.e., leaving the letter Nun unpronounced. You also should be careful not to answer Amein before the one reciting the berachah has concluded the entire berachah, because this is termed a hasty Amein. You also should not delay the answering of Amein because this is an orphaned Amein. Rather, immediately upon the conclusion of the berachah, you should answer Amein. You should not raise your voice louder than the one who recites the berachah, as it is said: "Declare the greatness of Hashem with me and let us exalt His Name together."²³Psalms 34:4.