Japa means repetition and mala is a string of 54 or 108 beads with one bead as the summit or head bead called a sumeru. Malas are used as a tool to help the mind focus on meditation, or count mantras in sets of 54 or 108 repetitions.
The mala is traditionally held in the right hand, however your dominant hand is the one more comfortable for you to use it. You can try in two ways : in one method, the mala is hanging between the thumb and the ring finger. The second finger is used to rotate the mala by one bead toward oneself with each repetition of breath or mantra. In the other method, the mala is hanging on the middle finger, with the thumb used to rotate it, one bead at a time. You will notice there is hand knotting between each bead, this is meant to help ease the practice of moving from bead to bead. On each bead, take a deep inhale and exhale. Then move to the next bead. Deep inhale and exhale. Or on each bead, inhale saying an affirmation like I am exhale saying that. However you do it, do it mindfully.
*Book to read: I Am That it is a compilation of talks on Shiva Advaita (Nondualism) philosophy by Sri Nisargadatta Majaraj, a Hindu spiritual teacher who lived in Mumbai.