How can one do teshuvah for a blemish of the covenant?

Greetings, 

First, one must return in complete teshuvah for the sin, that is, regret over the sin, verbal confession, and acceptance for the future not to return to this sin ever again (Rambam, Hilchot Teshuvah 2:2). Verbal confession means that one must say: "Please, Hashem, I have sinned, I have done wrong, I have transgressed before You, and I did such-and-such, and behold, I regret and am ashamed of my deeds, and I will never return to this matter" (Rambam, ibid. 1:1). And in order for the repair to be complete, he should accept upon himself, without a vow, to increase his Torah study each day, more than he was accustomed to until now. 

Sources: See Sefer HaTanya (Iggeret HaTeshuvah, chapter 9), where he wrote that because the blemish of the covenant through the emission of seed in vain, and certainly through sexual immorality or other Torah or rabbinic prohibitions against sexual relations, blemishes the mind, its repair is to engage in Torah, for from wisdom it comes forth. And this is what is written in Tanna Devei Eliyahu (note: I did not find it at the moment, but it is found in Vayikra Rabbah, section 25, paragraph 1): a person transgressed and became liable to death before the Omnipresent; what should he do and live? If he was accustomed to read one page, let him read two pages; to study one chapter, let him study two chapters, etc. And this is like the parable of a rope that was cut and then tied again, where at the place of the knot it is doubled and multiplied. And so it is with the rope of his inheritance, etc. See there. Also see Responsa Maharam Shik, part 1 (end of siman 58), who proved from Zohar Ruth (letter 12) that teshuvah for this sin is effective together with Torah study, and that from this it is proven that what is written in the Zohar (Parashat Vayechi) that teshuvah does not help for this sin means without Torah study. See also there, part 3 (in the index to siman 268, s.v. bedavar), where afterward he found in Rashi on Ezekiel (chapter 23, verse 37, in the gloss) that this too is explicitly stated there. Likewise this is explained in Yabia Omer, part 1 (Yoreh Deah siman 14, letter 14), and in his work Chazon Ovadia, Yamim Noraim (page 218). Also see Sefer Keter Rosh (letter 133) in the name of the Gra, zt"l; Aglei Tal (in the introduction, s.v. ve-al pi); Mishnah Berurah (siman 715, subparagraph 3); and what was written on this matter in Responsa Adret Tiferet, part 3 (siman 56). Also see Responsa Igrot Moshe, Orach Chaim, part 4 (siman 116), and part 6 (siman 40), where he wrote the order of teshuvah for the sin of masturbation and emission of seed in vain. 

With blessings, 

Hillel Meirs