Assalamualaikum ustaz. What is the ruling of reciting Amin loudly after al-Fatihah recitation in congregation? And what is the right methodology of reciting amin according to the sunnah?
Waalaikumussalam wrt. wbt.,
Alhamdulillah, praise and gratitude to Allah SWT for His countless blessings for us all. Praise and salutations to our beloved Prophet Muhammad PBUH, his family, companions, and all those who follow his footsteps until the Final day.
First, we should know that reciting “Amin” after the recitation of surah al-Fatihah for each individual who prays is sunnah. This means after Allah SWT’s statement: (وَلَا الضَّالِّينَ), it should be followed with the word “Amin.”
Likewise, it is sunnah to recite “Amin” loudly in prayers of which its recitation is loud and in a low voice in prayers, its recitation is in a low voice, while the makmum recite it loudly following the imam. 
Scholars have differing opinions regarding the meaning of the phrase “Amin”. However, the majority of scholars as cited by Imam Ibn Kathir stated that the meaning is (اللَّهُمَّ اسْتَجِبْ لَنَا) which means “O Allah, grant us.” 
Furthermore, Imam al-Nawawi also stated that it is sunnah for the imam to pause (a short time) between the recitation of al-Fatihah and “Amin” so that people will not think that the “Amin” is a part of al-Fatihah. 
While Habib Hasan bin Ahmad al-Kaff said it is sunnah for a person praying to pause between the recitation of al-Fatihah and “Amin” for a duration of the recitation of “Subhanallah”. 
The Ruling of Reciting Amin After al-Fatihah
Coming back to the above question, the recitation of Amin is not from the recitation of surah al-Fatihah and it is sunnah.
In answering the above question, we present the statement from the book al-Fiqh al-Manhaji (1/152), of which among others stated: “Reciting Amin after the recitation of Fatihah after Allah SWT’s statement (ولاَ الضَّآلِينَ), followed by the word Amin means: O Lord, grant it.”
This is based on a hadith from Abu Hurairah RA, Rasullullah PBUH said:
إذا قالَ أحَدُكُمْ: آمِينَ، ( وفِي رِوَايَةِ عِنْدَ مُسْلِمٍ: فِى الصَّلاَةِ) والْمَلائِكَةُ في السَّماءِ: آمِينَ. فَوافَقَتْ إحْداهُما الأُخْرى، غُفِرَ له ما تَقَدَّمَ مِن ذَنْبِهِ.
“If any one of you says: ‘Amin’ and the angels in Heaven say Amin, and the one coincides with the other, his previous sins will be forgiven.” 
The next hadith from Abu Hurairah RA:
إِذَا أَمَّنَ الإِمَامُ فَأَمِّنُوا فَإِنَّهُ مَنْ وَافَقَ تَأْمِينُهُ تَأْمِينَ الْمَلاَئِكَةِ غُفِرَ لَهُ مَا تَقَدَّمَ مِنْ ذَنْبِهِ
“Say Amen when the reciter (i.e. the imam) says it, for the angels do so, and if anyone’s utterance of Amen synchronises with that of the angels, he will be forgiven his past sins.” 
Likewise, in another hadith from Abu Hurairah RA:
كَانَ رَسُولُ اللَّهِ صَلَّى اللهُ عَلَيْهِ وَسَلَّمَ إِذَا تَلاَ (غَيْرِ الْمَغْضُوبِ عَلَيْهِمْ وَلاَ الضَّالِّينَ) قَالَ: آمِينَ. حَتَّى يَسْمَعَ مَنْ يَلِيهِ مِنَ الصَّفِّ الأَوَّلِ
“When the Messenger of Allah (ﷺ) recited the verse “Not of those with whom Thou art angry, nor of those who go astray,” he would say Amin so loudly that those near him in the first row would hear it.” 
The hadith narrated by Ibn Majah added:
فَيَرْتَجُّ بِهَا الْمَسْجِدُ
“…and the mosque would shake with it.” 
May Allah SWT grant us all understanding in fulfilling the commandment of prayer properly. Amin.