Hesychasts are those who ceaselessly practice the Jesus Prayer/the invocation of the Most Holy Name of our Lord Jesus.
In Orthodox monastic communities, it is very often the case that Hesychasts will pray the Jesus Prayer almost exclusively i.e. they will pray it several thousand times a day in place of the Daily Office (or those parts which they do not participate in with other monastics in their monastery) and otherwise they will say it non-stop.
They will be under the guidance of an Elder who will carefully ensure that they don’t fall into “prelest” or a kind of self-delusion, and that their prayer lives are balanced out with spiritual reading (Scriptures and the Philokalia in the first instance), regular attendance at the Divine Liturgy and Holy Communion etc.
Hesychasts may even engage in certain breathing techniques, although these are not necessary.
St Ignatius Brianchaninov, a great teacher of the Jesus Prayer, outlines some things a Hesychast/monastic needs for the purpose of ceaseless prayer in the Name of our Lord Jesus Christ:
A low stool to sit on
A prayer rope/lestovka i.e. prayer beads of some sort to keep count
a wet cloth to wipe one’s forehead etc.
a quiet place, usually the cell and the like
He then advocates that one just begin saying the Jesus Prayer with a pause in between each time the Prayer is said. According to St Ignatius, it should take half an hour to say the Prayer 100 times but other rules suggest a quicker recitation.
6,000 Jesus Prayers would replace the book of Psalms and 3,000 would replace the Daily Office (3,000 is the minimum with the maximum about 4500). For those who would like to do something like this, perhaps while on a retreat, it is good to have an abacus handy!
Alex