The Sankha Sutta is one of the best sutta's I know of that provides instructions on how to transcend and overcome the effects of past unskillful kamma.
http://www.accesstoinsight.org/tipitaka/sn/sn42/sn42.008.than.html
This is how there comes to be the abandoning of that evil deed.
This is how there comes to be the transcending of that evil deed. ...
when the awareness-release through equanimity is thus developed, thus pursued, any deed done to a limited extent no longer remains there, no longer stays there."
buddhism.stackexchange.com/users/4742/Kaveenga Wijayasekara
Depends on the tradition, but there are some well described ways, some purification ways.
For example, in vajrayana buddhism or tantra you could do the Vajrasattva practice for karma purification purposes.
buddhism.stackexchange.com/users/7192/rodzun
Of the 6 fundamental things about karma that Buddha said we should know, the 6th one is the cessation of karma.
The Nibbedhika Sutta (AN 6.63) says, And what is the cessation of kamma?
From the cessation of contact is the cessation of kamma; and just this noble eightfold path — right view, right resolve, right speech, right action, right livelihood, right effort, right mindfulness, right concentration — is the path of practice leading to the cessation of kamma"
buddhism.stackexchange.com/users/6999/sargon
There are few ways you can do this: Increase counteracting or store of good Karma (see: Loṇa,phala Sutta ) Develop habitual good karma as these tend to counteract occasional somewhat grave bad karma ( Maha Kamma,vibhaṅga Sutta ) Karma is extinguished when felt 1 , hence experiencing the past Karma effective now
you reduce the store of past karma.
This is not by self mortification but not letting past
Karma surfacing gaining strength to give more adverse results later
, i.e., experience it when the seed of karma gives its 1st sproute than waiting for a forest to grow.
2
In order to do this whenever you experience pleasant, neutral or unpleasant you should be fully aware of the feeling without craving or aversion knowing its arising and passing nature or impermanent nature if you cannot see arising and passing of phenomena.
( Pahāna Sutta , Avijja Pahana Sutta 2 ) 1 Loṇa,phala Sutta ‘Whatever experienceable karma [that do entail a consequence] that a person does, he would experience the result of that karma [that is, whatever fruits he reaps, they would accord with his karma] 2 Karmas which cause calamities in like has a snowballing effect.
It surfaces as a minor experience (e.g. repentant memory) to which you react to reinforce it, each time surfacing with larger and stronger effect.
buddhism.stackexchange.com/users/295/Suminda Sirinath S. Dharmasena
There the medicine: The Healing Power of the Precepts
And here are nice stories around this issue: The Healing of the Bull: A Story Prisoners of Karma:
A Story by Suvimalee Karunaratna
buddhism.stackexchange.com/users/11235/Samana Johann
I hope you feel no bitterness towards anyone.
this is one of the principles of Buddhism.
everything has a reason.
If there is sorrow that you have to experience, then there is a root cause for it too.
It is not the fault of the boys you used to know...
It is not the fault of the husband, or the relatives....
The pain within you is the result of a pain you have given others in some previous birth.
I hope you understand what I'm saying.
How you react to the pain is VERY IMPORTANT.
You can understand the dhamma behind the pain.... or you could start blaming everyone else...
If you choose to blame everyone else..... then the cycle of Hate,Blame, Suffering continues.... If you chose to UNDERSTAND THE DHAMMA behi nd the suffering....
then you can use the four noble truth principle and ARYA MAITHREE to end this suffering.
If you understand the root cause to be "suffering you caused others in the past"....
then apply ARYA MAITHREE towards all beings you may have associated in the past....
now that you understand the DHAMMA and you are a follower of BUDDHA in this life it would be possible for you to get compassion for any wrongful deeds that you may have caused in the past for others.... Theruwan Saranayi..
buddhism.stackexchange.com/users/None/
As we all agree none of us have a white past, we've all have done some bad thing in our past before coming to the path and in previous lives.  So how should we use the good karma we generate today toreduce the impact of bad karma from previous lives and from our past?  I've heard that this is possible.
Reducing the power of a bad karma
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The Sankha Sutta is one of the best sutta's I know of that provides instructions on how to transcend and overcome the effects of past unskillful kamma. For example, in vajrayana buddhism or tantra you could do the Vajrasattva practice for karma purification purposes. There are few ways you can do this:   Increase counteracting or store of good Karma (see:  Loṇa,phala Sutta )  Develop habitual good karma as these tend to counteract occasional somewhat grave bad karma ( Maha Kamma,vibhaṅga Sutta )  Karma is extinguished when felt 1 , hence experiencing the past Karma effective now. The Sankha Sutta provides instructions on how to transcend and overcome the effects of past kamma.   In Vajrayana Buddhism or tantra you could do the Vajrasattva practice for karma purification purposes. The noble eightfold path — right view, right resolve, right speech, right action, right livelihood, right effort, right mindfulness, right concentration — is the path of practice leading to the cessation of kamma. Increase your store of good Karma.  Develop habitual good karma as this tends to counteract occasional serious bad karma. Whatever karma  that a person gives, he would experience the result of that karma (i.e. he reaps the fruit of his karma.  2  negative Karmas could have a snowballing effect. The best medicine is The Healing Power of the Precepts .
The Sankha Sutta provides instructions on how to transcend and overcome the effects of past kamma.   In Vajrayana Buddhism or tantra you could do the Vajrasattva practice for karma purification purposes. The noble eightfold path — right view, right resolve, right speech, right action, right livelihood, right effort, right mindfulness, right concentration — is the path of practice leading to the cessation of kamma. Increase your store of good Karma.  Develop habitual good karma as this tends to counteract occasional serious bad karma. Whatever karma  that a person gives, he would experience the result of that karma (i.e. he reaps the fruit of his karma.  2  negative Karmas could have a snowballing effect. The medicine is The Healing Power of the Precepts .