Vratyastoma, is a ritual performed by Vratyas (people who have failed to perform Upanayana in time) to readmit themselves to the fold of Varnashrama Dharma. Many Westerners who convert into Hinduism perform this ritual.
This is what this site says about this ritual:
The tANDya brAhmaNa, and dharma shAstra texts as well, mention the ritual of vrAtyastoma to bring back vrAtyas into the fold of varNAshrama dharma. These vrAtyas were groups of people in ancient times who followed a quite unorthodox lifestyle, with few restrictions regarding food. Nor did they have an upanayana and study the Vedas. The vrAtyastoma, which is a set of four rituals, is performed to bring the vrAtyas into the fold of varNAshrama dharma. For example, the kAtyAyana shrauta sUtra states, "व्रात्यस्तोमेनेष्ट्वा व्रात्यभावाद्विरमेयुः । व्यवहार्या भवन्ति ।", by performing the vrAtyastoma, the vrAtyas lose their vrAtya status and become eligible for social life with (followers of varNAshrama dharma). The Apastamba shrauta sUtra also deals with the vrAtyastoma ritual. There is also a work exclusively devoted to such "conversion" called the vArtyatA-shuddhi-saMgraha, published by Chaukhamba. The vrAtyastoma is performed in the laukika-agni.
In modern times, some "innovations" to accomplish conversions or re-conversions have been used. I found one such ritual in a Marathi book titled "शास्त्र असे सांगते" (the shAstra says thus), which discusses how a person from another religion can become a Hindu. Some steps in this ritual are Panchagavya prAshana, Achamana, sankalpa, discarding the old name and taking up a new (Hindu) name, Ganesha-VaruNa pUjA, karNa vedha (piercing the ears), puNyAhavAchana, mangala nIrAjana, panchAyatana pUjA, gItA paThana, abhiSheka of the person with water from the Ganga and other rivers and the water from the Kalasha, dakShiNA dAna to the purohita, (dvir)Achamana, AshIrvAda-grahaNa from elders, and sahabhojana, eating with all the attendees.
The same site says:
The vratya stoma is described in the first 4 sections of the 17th chapter of the pa~nchaviMsha brAhmaNa. The stoma has been described as a means of admitting non-Aryans to the Aryan fold but this is not clear from the vedic text describing the rite. A summary of the brAhmaNa discourse is given below: The vrAtya stoma’s frame tale goes thus. The devas went to svargo lokaH. The gaNas of the dreaded The god were left behind leading the life of vrAtyas. They reached the spot where the devas had ascended to svarga but they neither found the stoma nor the Chandas by means of which they may join them. Then the devas told the maruts deliver the attendents of rudra the needful so that they may reach us. To them the maruts delivered that stoma with the 16 mantra chant which is the cryptic anuShTubh. Those who lead the life of a vrAtya are verily destitute or left behind because they neither practise the vedic study nor farming nor trade. It is by the stoma of the maruts that they prosper. For the rite he deploys the chant ” adha hi indra girvaNaH: For o indra who delights in the chants`(RV8.7-9)” which are in the kakubh Chandas. But the kakubh is an unequal Chandas for the sAmans. So he shall perform the shifting transformation on unequal padas of the kakubh to get the equalized verses for the song to the maruts known as the dyautAna sAman.
When the gR^ihasta chants the nidhana of this song it must end in the word “indra” musically uttered. The vrAtyas would be excluded from the prosperity if they were to use this nidhana. Hence they must replace indra in the nidhana of the song with the anirukta nidhana which goes thus with the following mystic stobha: au^2 3 ho^1 2345 ; i.e. falling from the highest pitch to the second last svara of the regular saman scale. The sacrificial oblations to the maruts may be made with the series of chants with 4 stomas with 16 mantras. The structure of the chants in the rite with respect to the the number of mantras they contain is thus: 9, 15, 15, 15, 16 : 16, 17, 17, 17, 16 : 16, 21
This rite is supposed to expitiate those who have eaten abhojya food as though the brAhmaNa’s food, those who speak in corrupted sanskrit, who have perform unjust acts, who despite being vrAtyas speak in Chandas.Thus, while there is an element of prAyshchitta in the prathama vrAtya stoma does not seem to be for non-Aryans.
I want to know how is this ritual performed. Does the Tandya Brahmana or any other dharmasastras say anything regarding how this ritual is supposed to be performed?