Swami Shivapadananda Puri explaining how to worship Lord Hanuman using the mantra, ‘AUM Hanumate Rudraatmakhaaya Hoom Phat.’
Rudra is Shiva, atmakhaaya - Shiva’s atman, Shiva’s light, Rudraatmakhaaya hoom phat.
This is how this mantra came about, is written down:
Once, the all-compassionate Mother of the universe, Sri Parvati, asked Lord Shiva to reveal a Hanuman mantra-yantra for the good of the world. Mantra is words you see, and yantra is the drawing. [Swamiji repeats] Hanuman mantra-yantra, for the good of the world.
The equally compassionate Lord gave her the above yantra and twelve-lettered mantra with the following instructions:
After the purificatory rites, the sadhaka [spiritual aspirant] must inscribe this yantra on a copper plate or any other suitable surface. That includes paper, if you like. …and place it in front of him. After worshipping Hanuman, light an incense stick and wave it around the yantra and place it nearby. If possible, light a camphor near the yantra, but not on it.
Then, make your desire known in words. Talk to Hanumanji. Tell Hanumanji, ‘I’m doing this worship or the japa [repetition of His name] , take some water in your hand, put it there or if you’ve got no water, just say, ‘Hanumanji I’m doing this yantra so my sickness may be cured,’ or ‘May there be progress in my education. Or, ‘Hanumanji, I find a lot of disharmony in my family. May there be harmony.’ ‘O Hanumanji, my mind is restless, let it be restful.’ Anything that you like - and then do this.
Now, number one: to accomplish a specific desire in a given time, repeat the manta one hundred thousand times. It can be done in one day or over a period, repeating one thousand times every morning and a thousand times every evening.
Two: For the general good, after worshipping as before, repeat the mantra 108 (one round of a mala - Hindu prayer beads) or one thousand times in the morning and in the evening. [basically, 10 full malas of mantra repetition each time]. In time, all your undertakings will be blessed.
To have Hanumanji’s darshan [have Him reveal Himself to you], repeat this mantra every night for one hundred thousand times, until he appears.
You may perform this in a clean corner of a room, in a Hanuman temple, in solitude or on a mountain, a forest or on a river bank. It is essential to observe mind and sense control brahmacharya [celibacy in thought,word and deed] while performing worship and observing the vow. Remember, Hanumanji is the eleventh incarnation of Lord Shiva, and he is the greatest devotee of God. Worship Him, contemplate and meditate on Him and He shall fulfil your desires.
If you desire to have moksha [liberation from the cycle of birth and rebirth] through Him, He shall graciously fulfil that, too. Hari AUM Tat Sat.