I want to change my Varna from Shudra to Brahmin, what is the procedure as per vedas or other authentic book.
Varna is a universal concept and applies to all of humanity. It is a measure of character. Currently Hindus determine Varna by birth and this Varna by birth is called caste in popular usage. A Mahabharata passage from Anusasana Parva Section CXLIII rejects the idea that Varna is by birth.
Maheshwara said, ‘..Neither birth, nor the purificatory rites, nor learning, nor offspring, can be regarded as grounds for conferring upon one the regenerate status.Verily, the conduct is the only ground. All Brahmanas in this world are Brahmanas in consequence of conduct. A Sudra, if he is established on good conduct, is regarded as possessed of the status of a Brahmana. The status of a Brahma, O auspicious lady [Uma], is equal wherever it exists. Even this is my opinion. He, indeed, is a Brahmana in which the status of Brahma exists – that condition which is bereft of attributes and which has no stain attached to it. of human beings in four orders dependent on birth is only for purposes of classification.The boon giving Brahma, when he created all creatures, himself said that the distribution of human beings in four orders dependent on birth is only for purposes of classification.'
Mahabharata Anusasana Parva Section CXLIII
Since varna is determined by conduct it is possible to change varna.
Change of Varna
Narada said, 'If in members born in a certain Varna the qualities pertaining to another Varna are seen, they (the former) are to be classified as belonging to the latter Varna.'
Srimad Bhagavata Purana VII.11.35
Sage Pulastya's views on how to become a Brahmana
Sage Pulastya said,"..by vows, by investiture of the sacred, by fasts, by rites, and by Mantras, one becometh a Brahmana."
(Mahabharata, Aranya Parva LXXXIII)
Only he who has purified himself by means of Gayatri Japa can be called a pure Brahmin. ….
Shiva Purana, Vidyesvarasamhita, 15.18
I am supplementing my answer with actual examples of persons who have changed Varna.
Examples of Change of Varna in Hindu scripture
Bhagavan Rishabha, realizing that the region of his advent was a place dominated by Vedic rituals, adopted the life of a religious student under a teacher with gifts, came back home with his blessings. He adopted the householder’s station of life in order to teach the world about the duties of that order, observed all the ceremonials and duties laid down in the scriptures, married a girl named Jayanti given to him by Indra, and begot by her a hundred sons equal to himself in all respects. Of all these sons, Bharata was the eldest and noblest. This Ajanabha Varsha came to be known after him as Bharatavarsha. Next to him, the eldest nine other sons ….. were elder to the remaining ninety. Among these ninety, another nine … became great devotees and teachers of the Bhakti cult. ….. The remaining eighty one of the brothers, who were humble in nature, learned in the Vedas, adepts in sacrificial rites, and extremely pure through their observances, became Brahmanas according to their father’s instruction.
Srimad Bhagavata Purana, V.4.8-13
At Kamyaka, Kusika’s son had quaffed the Soma juice with Indra. Then abandoning the Kshatriya order, he began to say,’‘I am a Brahmana’.
Mahabharata, Vana Parva, Section LXXXVII
If you have reached here then you need to first check if your claim that you are a shudra is by birth or by conduct. You believe you are a shudra because your parents told you so. Ask your parents if they studied your conduct and then gave you a name appropriate for a Shudra or they believed they are shudras by birth because of their name and hence they named you and told you that you are a shudra. If as I suspect that you think you are a shudra because of birth then you should give up your claim that you are a Shudra. The actual position is that you don't know what is your actual varna.
You want to become a Brahmin. Then you can do some of the things suggested by the Sage Pulastya or do japa of Gayatri obtained from a Guru and become a Brahmin by conduct.
I appreciate that you have openly asked question. But I never saw anyone asking how to convert from Kshatriya to shudra or from shudra to vaishya or from Brahmana to vaishya etc? Why?
Vedas have revealed that 4 varnas are from God only. As environment, challenges and needs keep on changing in KALI YUGA automatically one may not feel what VARNA he/she must practice. At this context it is better to stick towards one's swadharma to obtain greatest as MOKSHA.
Treating/considering oneself very bad by birth is NOT CORRECT. Earth is a very great place of abundant resources and joy. One must enjoy it.
All four VARNAs must worship GOD through their way to possible extent of their strength.
Firstly, being a pure devotee is even above being a Brahmana or being born in a great devotee lineage (and not being a pure devotee). In the Bhagavata Purana it has been mentioned that one’s actions and personality in their present birth determine their caste. Someone born in a ‘Brahmana family’ who is doing business would be considered to have a Vaishya caste(Part 7, Chapter 11, Verse 35).
The belief that caste is by birth is something the society has created, and personally I believe the British had a great hand in creating this system. Be a pure devotee, and if you want to be a Brahmana do Brahminical duties.
You may face opposition by Brahmanas themselves, and when Shri Krishna came as Caitanya Mahaprabhu 500 years ago he himself said that a lot of Brahmanas are power hungry and foolish (thinking themselves higher than a pure devotee).