In general, we atone by submitting our prayers to Perumal seeking His pardon. One does it exclusively by performing prayaschitta sharanagati.
Scriptures have provided atonements for each misdeed. If we are aware of the misdeeds, then we can atone accordingly, or we can recite the following verse from Swami Desikan’s Nyasa Dasakam and pray to Perumal as such for atonement.
akrutyAnA ca Karanam krutyAnAm varjanam ca me |
kshamasva nikhilam deva pranatArtihara prabho ||