I posted an article on Prayaschitta, Atonement for wrong actions, where I have listed some of the Sins, as decided by Hinduism and dealt in a general way
about Prayaschitta, Atonement
More details on the Prayaschittas are listed here.
Please check with your family priest for clarification.
I have been able to find Prayaschitta for most of the Sins.
I have not been able to find any for neglecting Sandhyavandana.
I think the Sandhyavandana was performed so regularly then, people never imagined that people would miss it.
However, the Prayaschitta Argya in the Sandhyavandana should do as atonement.
The very thought of regretting the non performance of Sandhyavandana is in itself an atonement.
After performing the Prayaschitta Argya and chanting 1008 Gayatrris, one may start performing Sandhyavandan daily.
This consists of taking food for three days only in day time followed by three days of food only in night time, followed by three days of food once , if offered without begging which is followed by starving for three days. This takes a period of 12 days to observe.
XV. Pada Kruchra
The procedure of Pada (quarter) Kruchra
This consists of taking food for one day in day time only, followed by one day food at night time only , followed by one day one time food, if available without begging and one day of starvation. This takes a period of 4 days to complete.
XVI. Ardha Kruchra
The procedure of Ardha (half) Kruchra
This consists of taking food for one day in day time only, followed by one day food at night time only , followed by two days one time food, if available without begging and two days of starvation. This takes a period of 6 days to complete.
XVII. Athi Kruchra
The procedure of Athi (more) Kruchra
This consists of taking only one hand full of food once in three days in day time, followed by three days at night time followed by three days if available without begging. This is to be followed by three days of complete starvation. This takes a period of 12 days to complete. Some sages permit only one mouthful of food but Sage Parasara is kind enough to permit one handful of food.
XVIII. Kruchradhi Kruchram
The Kruchram of Kruchrams
This consists of drinking only water once during meals time for three days in day time, followed by three days at night, and followed by three days without begging, which would be followed by three days of complete starvation. Sage Yagnavalkya says that, taking once only milk for 21 days is Kruchradhi Kruchram. This is easier.
Thaptha Kruchram is taking once for three days hot water once, followed by three days of once hot milk followed by three days of hot ghee, which has to be followed by three days of complete starvation.
Santhapana Kruchram is taking Cow’s urine , Cow dung , milk , curd, Ghee and Kuchotha (?) in that order once for one day each , followed by one day of starvation.
Starving for 12 days is called Paraga Kruchram. Suppose we live for one month only on fruits , it is called Phala Kruchram, Suppose we take only gruel made of Barley for one month it is called Yavaka Kruchram.
Reciting Agamarshana Suktha followed by Thrishavasa (?) snana and observing fast for three days is called Agamarshana Kruchram.
Mortification for 30 days
This is of two types – Pippeelika Madhyam (Ant middle) and Yava Madhyam (Barley middle.
Pippeelika Madhyam is fat in the beginning and end and slender in the middle and Yava Madhyam is thin in the beginnings and end and stout in the middle.
This Is Pipeelika Madhya Chaandrayanam
Start on Prathama of Krishna Paksha. Take 14 handful of food on that day. On the second day take 13 handful and so on and observe fast on Amavasya. On Shukla Prathama take one hand full and next day two hand full and so on. On Pournami day take 15 handful.
This is Yava Madhya Chaandrayanam
Start on Shukla Paksha Prathama. Take one handful on the first day, two on the second day and so on for 15 days. On Krishna Paksha Prathama take 14 handfuls. Daily reduce one handful for 14 days and on Amavasya observe fast.
Before beginning of these rites, you have to shave and give Dhana and Dakshina to Brahmins.
Taking three handful of food for one month and living a life of austerity is called Rishi Chaandrayanam.
Taking four handfuls during day followed by four handfuls at night for one month and leading a proper life is called Shisu (child) Chaandrayanam.
Taking eight handfuls for one month is called Yathi Chaandrayanam.
XX. Keshaam chith paapanam Prayaschitha
Redemptive acts for certain sins.
Parasara says that in the Kali age the redemption for Brahma Hathi dosha is to take bath in Rameshwaram. He has instructions for doing it properly . We should do Sankalpa and without slippers and umbrella walk and reach Rameswaram from our home. While going you have to beg and eat. While Begging you have to say , “I am a sinner, I have Brahma Hathi dosha, Please give me alms,”. We should never enter any house. We can take rest in river banks or cattle sheds, Frequently we have to describe the nature of sin committed by us to people. After reaching Rameshwaram , you have to take bath in Dhanushkoti and in all theerthas including Agni Theertham. After this we can to return to our village and give as Dhana hundreds of cows and feed hundreds of Brahmins.
More information at the Link quoted above,