The Shulchan Aruch (Orach Chayim 124:8) lists several situations of an improper response of "Amen" to a Beracha:
1) An "Amen Chatufa" refers to mispronouncing the word "Amen" as "Imen," as if there were a Sheva vowel, rather than Patach, underneath the letter Alef. It also means answering "Amen" too early, before the Beracha has been completed. One must ensure to properly pronounce the word as "Amen" rather than "Imen," and to wait until the Beracha is recited in its entirety before answering "Amen."
2) An "Amen Katufa," or "snipped" Amen, refers to a response of "Amen" without pronouncing the letter Nun at the end of the word. One must ensure to pronounce all three letters of the word.
3) An "Amen Ketzara," or "short Amen," means reciting the word "Amen" too quickly. One should recite the word in the amount of time it would take to say the three words, "Kel Melech Ne'eman," and no faster or slower than this duration of time. The Sages say that one who elongates his recitation of "Amen" is rewarded with a prolonged life. That said, one must ensure not to extend the response longer than the amount of time needed to say "Kel Melech Ne'eman."
4) The definition of the fourth category, "Amen Yetoma" (literally, an "orphaned" Amen), is subject to debate. According to the Rama, this refers to answering "Amen" without hearing the Beracha. For example, if a person walks into the synagogue and hears everyone answering "Amen," but he did not hear the actual Beracha, he should not according to the Rama join in their response, since he did not hear the Beracha. The Shulchan Aruch, however, disagrees, and permits reciting "Amen" even if one did not hear the Beracha. The term "Amen Yetoma," in his view, refers to a case of a person who recites a Beracha on behalf of another, so that the listener will fulfill his obligation by hearing the recitation, but he did not hear the entire Beracha. Only in such a case must one not recite "Amen" if he did not hear the Beracha; in all other cases, however, according to the Shulchan Aruch, one may recite "Amen" even if he did not hear the Beracha.
The Kaf Ha'chayim (Rabbi Chayim Palachi, rabbi of Izmir, Turkey, 19th century) writes that even the Shulchan Aruch would agree that one bears no obligation to answer "Amen" if he did not hear the Beracha. He merely permits responding "Amen" in such a case, while agreeing that one is not obligated to do so. Therefore, the Kaf Ha'chayim rules that in such a case one should preferably not answer "Amen," thereby satisfying both the view of the Shulchan Aruch and the position of the Rama.
Summary: One must ensure to pronounce the word "Amen" correctly, and to recite it only after the Beracha has been completed and in the amount of time needed to say the words "Kel Melech Ne'eman." One should preferably not answer "Amen" if he did not hear the Beracha.
