Jesus prayer also referred to as Prayer of the heart is one of the oldest prayers for christians.
There are various forms but the most common is "Lord Jesus Christ have mercy on me".
others use" Lord Jesus Christ, Son of God have mercy on me/us" or "Lord Jesus Christ, Son of God have mercy on me, a sinner".
All forms are correct.
By saying the name of our Lord Jesus Christ we ask for his help, protection, divine intervention and saving of our soul.
This prayer started with the fathers of the desert in Egypt with Evagrius Ponticus, an ascetic christian monk of the IV century. A theologian that left us many texts that are still a source of spiritual teaching for the modern world.
During the centuries the prayer has been practiced by monks especially in the eastern mediterranean region.
It's used as a base for hesychast monks that want to achieve divine stillness.
Later on it has been proposed to connect the prayer with the breath. However this is not needed to achieve stillness and might have an impact on your heart beating. Many fathers spoke against such a method due to its danger.
The Jesus prayer is widely practiced in Mount Athos.
Jesus Prayer became even more popular with the Philokalia Book in the XVIII century and the book "The Way of a Pilgrim" a classic in russian literature.
Jesus prayer is often prayed with prayer rope. Traditionally is in black wool with 100 knots. There are others with 33, 50, 70, 72, 300, 500 or 1000 knots/beads. Today you can find prayer rope also known as komboskini in Greek and Chotki in Russian in wooden beads, stones and other materials.
You can buy a prayer rope, komboskini at the Christian Gift Shop in Skala in front of the church of Agios Pnévmatos, Holy Spirit Church