How is the Rite of Peace done in your particular Church?
In the Melkite Church the priest turns to the people and says “Christ is among us!” (or the appropriate seasonal greeting) and the people respond “He is and He always will be!” (or the appropriate seasonal response). They then share this same greeting with each other while the concelebrating priests share this same greeting with each other, the deacons with each other and the bishops with each other.
After the praying of the Lord’s Prayer, the priest says with his hands extended, “Lord Jesus Christ, you said to your apostles: I leave you peace, my peace I give you. Look not on our sins, but on the faith of your Church, and grant us the peace and unity of your kingdom, where you live for ever and ever.”
(Domine Iesu Christe, qui dixisti Apostolis tuis: Pacem relinquo vobis, pacem meam do vobis: ne respicias peccata nostra, sed fidem Ecclesiae tuae; eamque secundum voluntatem tuam paceficare et coadunare digneris. Qui vivis et regnas in saecula saeculorum.)
We say Amen.
The priest, facing the people, says: “The peace of the Lord be with you always” (Pax Domini sit semper vobiscum).
We say: “And also with you” (Et cum spiritu tuo).
The priest or deacon says something to the effect of sharing the peace with each other (Offerte vobis pacem).
Among the priests and deacons the sign of peace is made with a psuedo-embrace and kiss…among the laity it varies according to local custom.
Scroll to about the 18:15 mark
That’s how the Syriac and Malankara Orthodox/Catholics do it.
The two Melkite parishes I have been to only do the Rite of Peace between clergy members of the same rank, priests with priests and deacons with deacons, nothing is shared among the laity.
Maronite practice is that the celebrant “takes” the peace from the altar and oblation and then passes it. As I recall, the traditional way was to touch the first two fingers of the right hand to the lips, and then touch the Altar (or the Altar Board) (“Peace to you oh Holy Altar of God”). Again fingers to lips and then lift the small veils (“palls”) and touch the paten and chalice (“Peace to the Holy Mysteries placed upon you”. At this point the peace was given to the concelebrants (if any) (“Peace to you, my brother in the priesthood” using the ritual embrace) then the deacon(s) (if any) or the sub-deacon(s) (if any) or in the absence of all the preceding, to the server, (Peace to you oh servant of the Holy Ghost) (Here the server would place his right hand on the edge of the Altar, palm down, and the celebrant would “give the peace” by touching the top of the server’s hand.) The last rank to receive it from the celebrant would transmit it to the next and so on, by means of a touch: the donor would have hands in the “praying hands” position and the recipient would place hands over those of the donor. The peace is passed among the congregation in the same way. During the passing of the peace, a diaconal admonition is sung. Note that the neo-Maronite way is somewhat simplified, but essentially similar.