This is for males who had completed the Sacred thread ceremony. There are mild variations in the formalities and the mantras. Those who follow and perform will have their own tradition. It may be asked from the family elders or from the family/community priest in that place. The relevant priest is the best person who can guide, as he knows about different variations also.
It is referred as Avani Avittam by Iyers of TN and Kerala. It is referred so because generally it falls on the Tamil/Malayalam month Avani and on the day with star Avittam. The Vedic name in Sanskrit is Upakarma.
It is a wrong notion propagated by people who had half baked knowledge that it is a thread changing function only. It is not that. Sacred Thread has to be changed before any ceremony and also whenever the thread is dirty, weak, broken, splintered or damaged otherwise. So on Avani Avittam day also the thread is changed to a new one. That is all.
Basically it is a 'Tharpan' giving function to one's Pitrus or deceased ancestors, the Devas(gods) and the Rishis. The function includes an open atonement for the sins committed, by not performing the expected duties and rituals as per the Vedic scriptures and texts; the deviations and aberrations committed from the expected path etc. It is atonement for sins by errors of commission and omission of Shastra-prescribed way of life. Specified Mantra is chanted about one thousand and eight times. The function also includes a homa (yajna fire) and Vedic chanting by all participants guided by the chief priest conducting it.
As such a divorced male person in a community that follows this system also has to perform Upakarma/Avani Avittam.
(Note: Kindly correct the word as 'Avani Avittam' in the thread)