Om Namo Bhagavate Raghunandanaaya Rakshogna Vishadaaya Madhura Prasannavadanaayaa Amitathejase Balaaya Raamaya Vishnave Namah
OM namO bhagavatE raGunaMdanAya rakShOGna viSadAya madhura prasannavadanaayaa(a)mitatEjasE balAya rAmAya viShNavE namaH
ಓಂ ನಮೋ ಭಗವತೇ ರಘುನಂದನಾಯ ರಕ್ಷೋಘ್ನ ವಿಶದಾಯ ಮಧುರ ಪ್ರಸನ್ನವದನಾಯಾ(ಅ)ಮಿತತೇಜಸೇ ಬಲಾಯ ರಾಮಾಯ ವಿಷ್ಣವೇ ನಮಃ
ओं नमो भगवते रघुनंदनाय रक्षोघ्न विशदाय मधुर प्रसन्नवदनाया(अ)मिततेजसे बलाय रामाय विष्णवे नमः
OM namO bhagavatE raGunaMdanAya rakShOGna viSadAya madhura prasannavadanaayaa(a)mitatEjasE balAya rAmAya viShNavE namaH
ಓಂ ನಮೋ ಭಗವತೇ ರಘುನಂದನಾಯ ರಕ್ಷೋಘ್ನ ವಿಶದಾಯ ಮಧುರ ಪ್ರಸನ್ನವದನಾಯಾ(ಅ)ಮಿತತೇಜಸೇ ಬಲಾಯ ರಾಮಾಯ ವಿಷ್ಣವೇ ನಮಃ
ओं नमो भगवते रघुनंदनाय रक्षोघ्न विशदाय मधुर प्रसन्नवदनाया(अ)मिततेजसे बलाय रामाय विष्णवे नमः
The above mantra is one of rare one and according to texts this mantra has the power to grant 4 purusharthas (Dharma, Artha, Kama and Moksha)
It is said that great sages of ancient lore have used this mantra for attaining spiritual bliss and this mantra is said to confer child for childless couples.
It endows the person with knowledge, wealth, righteousness and a sense of detachment from unnecessary worldly ties
It is also said that this mantra should be taken from a guru and success can be achieved only through initiation.
In the present world getting an accomplished Guru is very difficult. So what I suggest is that write down the mantra a sheet of copper (used for yantra) or on paper and place it next to the picture or idol f Lord Shri Rama. Perform suitable prayer to this mantra and idol by offering Incense, Camphor and offer food to the God.
Later visualize that you are getting initiated to this mantra from the Lord Shri Rama itself, by this way you are considering the Lord to be your Guru.
Start chanting this mantra daily for 1000 times without breaks in-between.
Please note that lord Rama is a Great god who upholds Dharma, So as you progress with this sadhana you will put into situations where you will have moral dilemma on doing what is right. Please be true to yourself and be righteous as this will be test of your devotion to the lord.
Ideally Rama mantras needs to be chanted 1 million times to reap its full benefit but you can start seeing changes once you complete 15000 chants of the above mantra.
I wish all the very best to those who will take this sadhana up.