Cleansing, praying, fasting, in the case that this has something to do with one or more actions, words or habits.
Read Sallust. All gods are like the sun, and we obscure ourselves from hiding from them. Redemption and renewal is only thought as a christian theme, but the cases for Oedipus and Herakles in mythology, and the orphic, eleusinian and samotracian mysteries in cult are good examples for how this theme was important for polytheistic culture as it is nowadays for the regular christian. Read the myths of the passions and actions of the Gods as symbols by how certain divine influences (and everything emanates from the gods) can be mislead and mishandled by we mortals, because of our frailty, neediness and ignorance. So pray to Apollo, Dionysus and Zeus Katharsios for purification (or the correspondent gods of your pantheon). In case of shame, anxiety and just the feeling of generalized unworthiness, approach any God praying to surpass this feeling born out of ignorance, and read about the history of the cults of your Gods, read their myths interpreted by neoplatonic pagan theology, beginning by Sallust and reading also Iamblichus, Porphyry and Proclus.