Hesychasm - what exactly is it, and how does one practice it?

Hesychasm - we sometimes hear about it, but what exactly is it, and how does one practice it? The general idea is to acquire an “inner stillness,” putting aside our senses, and withdraw inwards to pray, frequently the Jesus Prayer - “Lord Jesus Christ, have mercy on me, a/the sinner.” St. Gregory Palamas who we commemorate on this second Sunday of Lent, defended this practice against a more intellectual approach to prayer typical of Roman practices, e.g., the rosary mysteries. This is not to say that this form of prayer consists of mere hollow/ vain repetition, but rather that we approach a mystical and/or meditative practice in our recitations of the Jesus Prayer, more of which can be read about here.