Tuesdays and Saturdays are especially auspicious for worshiping Lord Hanuman. He's particularly pleased when one also worships Lord Rāma. Here is a prayer for Lord Hanuman...
ruta tulya vegam
ndriyam buddhi-matam vá
nara yutha mukhyam
Shri Rāma-dutam shá
padye || (accent in Sanskrit is usually
on the 2nd to last syllable)
The meaning of the Mantra is as follows.
I take refuge in Sri Hanuman, the one, who is swift as the mind and fast as the wind. He is the master of the senses and honored for his excellent intelligence, learning, and wisdom. He is the son of the wind god and chief among the Vanaars. One who is part of the Devas incarnated in the species of the monkeys to serve Sri Rama during his incarnation. Hence, to that Messenger of Sri Rama, I take refuge in him, by prostrating before him.
His gayatri (3 lines, 8 syllables) mantra:
Om Anjaneyāya Vidmahe
Tanno Hanuman Prachodayat
Let us meditate on the son of Anjani
May the son of the Wind give me intelligence
May Hanuman enlighten my mind.
The following mantra got me my job back (I was part of a lay-off, but they called me back). Start chanting this mantra on Thursdays and chant 11 times in the morning. I did it until my job was secured:
Om Shree Vajra-dehāya Rāma-bhakthāya Vayu-puthrāya Namostute
Obeisance to the one hit by a thunderbolt; the devotee of Rāma; son of the Wind.
Lord Hanuman has been a great friend to me.