Identify the problem
Identify the root cause of the problem first. It is logical that you may have hurt their feelings in the heat of the moment but when alone, look at the reasons which led to the fall-out. You may end up concluding that the situation could have been handled in a different way. The blame may not be entirely upon you, but it is important to understand that parents also make mistakes, and find it hard to admit. The process is not to identify the guilty party but to find ways on restoring the relationship.
You will need to be patient as it will take time to solve matters. Give the process some time, and in the meanwhile, start to indulge in a dialogue with your parents. At the beginning, the topics must not be relevant to the issue but with time, clearly state your intentions. Rather than going around the subject, it is essential that you and your parents are on the same wave length.
Conversation should take place at a suitable time. If you are not living with your parents anymore, then ask them to meet you for lunch or dinner, or visit their residence. If you are reluctant, then write a letter to inform them about your intentions. Give them time to respond.
In order for the relationship to work again, learn to forgive. Unless the issue concerns sexual abuse, one can surely fix the problem. Accept the way your parents are, and they too will be more than willing to forgive you. At this point, it is essential to remember the good times you spent with your parents.
Every relationship takes time to mend. In the meanwhile, make sure to be persistent. Prove it by actions where you are willing to do anything to gain back the trust of your parents.
Seek professional help
If your efforts don’t get you the results, it is wise to seek professional help. This way your parents will understand that you are serious and want to patch up big time.