1. Determine what your regret really is. It is important to step back from the feelings of regret and identify exactly what the regret is. Do you regret something you did or something you didn’t do? Something someone else did or did not do?
2. Ask for forgiveness and make amends. Apologize for any harm you may have caused others, and also forgive yourself. Be compassionate toward everyone involved, including yourself.
3. Accept the circumstances. Avoid blaming others but rather take responsibility for anything that you, personally, could have handled better.
4. Deal with toxic relationships. Sometimes other people cause us to do things that leave us with serious regrets. Do you have a toxic relationship that needs to be addressed or severed?
5. Grieve for your regrets. When we feel regret, we re-live guilt, sadness or anger over and over again. Allowing yourself to experience these feelings fully with the intention of moving forward can help you stop revisiting them.
6. Recognize what you have learned or gained. When you find yourself thinking of the regret, turn your thoughts to the things you have learned and the opportunities that are now yours - even if they are not what you would have preferred. There is always a lesson even in pain and sadness.
7. Write out a plan or agreement for yourself that identifies how you could avoid having this sort of regret in the future.
Source: http://www.wikihow.com/Overcome-Serious-Regrets (abridged)