In general, in addition to private acts of forgiveness, public expressions of forgiveness include forgiveness as an element in the second and forth movements of the Liturgy. Additionally a formal, public expression of forgiveness may also be performed as a Rite of Purification in the Catechumenate and Novitiate.
Also see Anointing, Confession, Exorcism, Restitution, Rite of Incorporation, and Rite of Purification.