From "In the Divine Service"...
The word Amen means “It is true” or “I believe this.” Favorite Bible and catechism answers to “What does Amen mean?” include “So be it,” “Yea, yea, it shall be so,” “This is a faithful saying,” and “This is most certainly true.” The word comes from Hebrew, but it is also used a lot in the Greek New Testament. Whenever Jesus says, “Truly, truly” (or “Verily, verily”), he is literally saying, “Amen, amen.”
You say Amen at the end of a prayer, because you mean it personally as your own worship and request to God, and you trust that God will grant your prayers in accord with His kindly will. “It shall be so.”
You say Amen at the end of a creed because it is your own confession of faith and you believe it; and at the end of a confession of sins because you really are a sinner as God’s word shows, and you really do repent and want God’s forgiveness. “It is so.”
You say Amen after a blessing or salutation because you want to claim that blessing for your own; “So be it,” or “Let it be so.”
You say Amen when the Pastor absolves you of sin, or gives you Christ’s body and blood, because you believe what God’s Word says about how the Lord Himself is dealing with you and cleansing your conscience of sin. Any past, present, or future historical fact, sacramental act, or spiritual reality that you must hold onto by faith, is an occasion for saying, Amen. Because the Amen means you believe, and by faith you receive.
There are many points in the liturgy where you, as a congregation or as an individual, are expected to say Amen. Look at the order of Divine Service. The invocation in the name of the Trinity calls for an Amen so that you all, not just Pastor, call upon Father, Son, and Holy Spirit to be present. Amen concludes the confession and absolution because your own sins are real and so is God’s forgiveness. Amen ends the Gloria (“Glory be to God on high”) because it is part creed, part praise to the Holy Trinity. You’ll notice that when a hymn ends that way, you are expected to stand (and say Amen, even though the hymnal doesn’t always say so).
The Collect of the Day ends with Amen: it is your prayer, and you should mean what you pray. The Creed ends with Amen because it is what you believe. You can say Amen to the sermon (or at least the blessing before and after it), if you have heard God’s Word taught in its truth and purity. The offertory ends in Amen because it comes from Psalm 51, and since Psalms are prayers to the Triune God, Christians always say Amen after them. The Prayer of the Church ends in Amen. The Lord’s Prayer ends in Amen.
The correct response to “The peace of the Lord be with you always” is not “And also with you,” but Amen because it is a blessing you claim for yourself, and it is based on the Words of the Lord’s Supper which have just been proclaimed. You sing Amen at the end of “O Christ, the Lamb of God” because it is a prayer. You could also say Amen when you receive the Lord’s body and the Lord’s blood, and certainly when you “go in peace.”
“Lord now let your servant” ends in Amen because it too is a prayer, and a sort of New Testament Psalm (from Luke 2). Besides, it ends with praise of the Triune God again. Then there are more prayers (Amen, Amen), and finally the climactic triple Amen follows the benediction, because the God of Moses and Aaron who gave this blessing in Numbers 6, is the Triune God who blesses you in Jesus Christ.
These are not the only times you can or should say Amen. It is up to you to say it; the Pastor should not say it for you, because it is really your response to what the Lord tells you through the Pastor.
Sure, you can overuse Amen. That’s what happens when you say it to things that do not matter, to things that are not true, or (as many Christians do) simply because their preacher knows how to excite their emotions. The rule of thumb is, if you can rely on something to be true, if it is a matter of faith based on God’s Word, say Amen!