You can chant these holy names of the Lord anywhere and at any time, but it is best to set a specific time of the day to regularly chant. Early morning hours are ideal. As you chant, pronounce the names clearly and distinctly, addressing Krishna in a prayerful mood. When your mind wanders, bring it back to the sound of the Lord’s names.
In the material concept of life, we are busy in the matter of sense gratification as if we were in the lower, animal stage. A little elevated from this status of sense gratification, one is engaged in mental speculation for the purpose of getting out of the material clutches. A little elevated from this speculative status, when one is intelligent enough, one tries to find out the supreme cause of all causes-within and without. And when one is factually on the plane of spiritual understanding, surpassing the stages of sense, mind, and intelligence, he is then on the transcendental plane. This chanting of the Hare Krishna mantra is enacted from the spiritual platform, and thus this sound vibration surpasses all lower strata of consciousness-namely sensual, mental, and intellectual. There is no need, therefore, to understand the language of the mantra, there is neither any need for mental speculation nor any intellectual adjustment for chanting this maha-mantra. It is automatic, from the spiritual platform, and as such, anyone can take part in the chanting without any previous qualification.
When you chant alone, it is best to chant on japa beads. This helps you fix your attention on the holy name. Each strand of japa beads contains 108 small beads and one large bead, the head bead. Begin on a bead next to the head bead and gently roll it between the thumb and middle finger of your right hand as you chant the full Hare Krishna mantra. Then move to the next bead and repeat the process. In this way, chant on each of the 108 beads until you reach the head bead again. This is one round of japa. Then, without chanting on the head bead, reverse the beads and start your second round on the last bead you chanted on.
Source: A.C. Bhaktivedanta Swami Prabhupada (2012 edition), “Message of Godhead”, Last Page
A.C. Bhaktivedanta Swami Prabhupada (2014 edition), “The Science of Self-Realization”, Page 168