Japa (Sanskrit word) means "to repeat" so this form of meditation involves repetition of a mantra and keeping count of those repetitions. The mantra must be carefully chosen: it should be awe-inspiring and meaningful to yourself and should also keep you engaged for a sufficiently long period of time.
It is considered easy because of these simple factors but that is a misconception. However interesting a mantra may be, it is eventually going to get tiresome.
The mind-numbing part of it actually helps the yogi focus but instead, s/he may focus on the silliness of the seemingly endless repetition. It won't take long to feel that all the chanting is going to be in vain! Choose a song, a music composition, or poem that you like, and are inspired by. It doesn't have to be a hymn but for heaven's sake don't choose Rap! Have a clicker counter or a rosary ready and you are all set. (The rosary is also referred to as "mala" - string of beads). Thus, the requirements for mantra meditation (as Japa Yoga is also called), are a suitable mantra and a clicker counter (or rosary).
However, there are a couple of other factors that you need to consider:
A. Readiness to take on a mindless task
B. Readiness to persist in that mindless task
Personally, I chose not to follow japa practice because of its repetitious simplicity. I didn't want to give up the physical pleasures of Kriya Yoga and Karma Yoga. So don't over-estimate the simplicity of this mantra repetition - eventually you will have to call upon immense discipline to persist in this yoga practice. I'm calling this a mindless practice - which it indeed is - but it also leads to a mindlessness that is much needed.
The socially cultivated and superficial mind needs to be eliminated.
The mind of mundane logic has to be decimated.
The mind of social indoctrination has to be destroyed.
Mantra repetition will stupefy you and lead you that level of mindlessness so that you vibrate on the level of pure consciousness. But this can take time! This repetition is not the same as repeating a prayer over and over again: mainly because a prayer is quite simple compared to a hymn or a chant. The lyrical and rhythmic aspects of songs, poems, chants, compositions, etc. are vital to this form of practice. Consider the following: you will never get breathless while praying, but you will get slightly out of breath while singing or chanting. Some amount of breath control is required and that's why some form of pranayama is involved while performing this yoga.
As you progress in this meditation, the mantra chanting will become automatic and take on one of two forms:
Chanting with Awareness and Chanting without Awareness.
Chanting without Awareness happens easily as you become familiar with the mantra and with your breath. You will continue with the exercise but your mind will be elsewhere. This is why the counter/rosary is necessary. It keeps your focus on the task and doesn't provide the mind any bandwidth to take on any other thought, thus ensuring Chanting with Awareness.
These are the simple techniques that - when mastered - will also help in achieving dhyana in Raja Yoga and Tantra Yoga. It is also one pathway (marga) of Kundalini Shakti Awakening.
According to the spiritual traditions of this yoga, the mantra itself plays an important role. It must be something that you have divined, dreamed of, and granted by your teacher. It's quite unlike that any of these will occur in the urban, modern world that we live in. That's why you need to put in some effort to research some song, chant, or classical composition that will appeal to your personal spiritual practice.
Explore your Bob Dylans and Beethovens and Berliozs and Bachs.
Don't give up!
You will find more interesting - and relevant - pieces of music/mantras here than indulging in some futile attempts to appropriate meaningless Sanskrit shlokas or some kirtan (a form of hymn) that you don't understand. Divinity comes from the practice of mindful participation. And this requires you to be familiar with every aspect of the mantra and the ritual of the Japa. In this context, understand also why the Japa is done in the following manners:
1. Loud Japa: Increases focus and enables reception of the mantra through your ears.
2. Silent/Whispering Japa: Helps with the performance of pranayama. Silent repetition of the mantra connects the prana to our higher consciousness.
3. Mindful Japa (Writing): Completely immerses you in the mantra by involving your hands. It's recommended that you choose a long mantra, song, or poem for this exercise. Consider writing Paradise Lost (John Milton) several times! Don't worry, many other people have done it and quite a few have even memorized the entire poem!
Sometimes the mantra can be the different names of a god. There are quite a few Hindu gods but only some of them have almost innumerable names. Some examples are Vishnu, Shiva, and Kali. One such chant is the Shri Kali Sahastranam Stotram which recites the 1008 names of the goddess Kali. It's interesting and intriguing to hear but obviously it's meaningless since you don't understand most of the words mentioned. I talk about it here to compare the vibrations of such chants to the vibrations of compositions from say Western Classical music. Somehow, both evoke sensations that go beyond words.
Going beyond words and into the domain of intuitive knowledge
is the goal of all meditation.
When performed with devotion - devotion to the technique and not to some deity - you will be rewarded with a sensation of gratitude. These are emotions that will naturally arise with sustained practice but sometimes they need to be recognized for what they are, and for that you need a yoga instructor or guru.
Sustained practice will also empower you with purity of thoughts by erasing false beliefs and irrational expectations. Bad habits, obsessive thoughts, and compulsive behaviors are eliminated. It's almost as if you are cleansing yourself through rigorous, sustained, persistent scrubbing with nothing more than a scrubber and some water.
Japa meditation increases awareness of yourself by making you aware of your potential to achieve anything through sheer repetition!