From GIRM (General Instruction of the Roman Missal)
**" ** 82. The Rite of Peace follows, by which the Church asks for peace and unity for herself and for the whole human family, and the faithful express to each other their ecclesial communion and mutual charity before communicating in the Sacrament.
As for the sign of peace to be given,
the manner is to be established by Conferences of Bishops in accordance with the culture and customs of the peoples. It is, however, appropriate that each person offer the sign of peace only to those who are nearest and in a sober manner.
"
Hugging, hand shaking, kissing, talking to each other, waving, turning ones back on the alter and tabernacle, etc., is not part of GIRM.
usccb.org/liturgy/current/revmissalisromanien.shtml
The above is for the ordinary Mass, not the extraordinary also call Tridentine, Traditional or Latin Mass which uses the 1962 Missal.
catholicnews.com/data/stories/cns/1100868.htm