In this suite of teshuvot from the mid-1970's, Rav Moshe Feinstein responds to anonymous questioners who were seeking to do teshuva for a variety of sins of a sexual nature, including homosexual acts, masturbation, an office affair (asked by the woman), and pre-marital sex (also asked by the woman).
There are several notable points about these teshuvot:
1) Rav Moshe's extreme sensitivity towards those asking the question, as he takes the basic stance that despite the severity of their sins, the fact that they are asking the question about doing teshuva indicates that they are clearly regretful of their actions and are thus on the right path.
2) Rav Moshe prescribes several actions for the penitents, including learning Torah, reciting Tehillim, and private confessions, based on the logic that actions are stronger than mere thoughts and that taking various practices upon oneself will serve as an inoculation against the thoughts that led to the various actions.
An interesting issue arose with the last case, where the woman who had had pre-marital relations was getting married and did not want her past misdeeds to be known to anyone other than her future husband. Rav Moshe permitted her to have the ketubah read the same as the ketubah of a virgin, based on the fact that since her husband knew the truth about her past and nevertheless accepted upon himself the responsibilities of a full ketubah, there would thus be no issue of the ketubah being false and there would be no need to even inform the mesader kiddushin of this fact.