1. Identify the issues that separated you. it could be the least little thing that escalated, or it could be an imagined slight. It could even be a deliberate and provocative head game -- with potentially deadly consequences. In some cases it may be necessary to bring in an intercessor or even an attorney.
2. Once you and the other person identify the issue that will result in reconciliation, then seek terms of remedy. If the other will not accept remedy, then there is no way to attain forgiveness. Sufficiently neurotic (or psychotic) persons might want you to suffer public humiliation -- or may presume wrongly that you would do that to them. Make it clear from the outset that such a thing is out of the question, neither to be offered or accepted.
3. If there are tangible damages to be settled, find that remedy that you can both accept.
4. Realize that there are a lot of bad feelings on both sides but you are trying to eliminate a long nasty feud that could cost you dearly later.
It does depend on the guilt and circumstances. Speaking from experience, I would say the best way is by apologizing and being honest and sincere about it. Knowing that the person you feel guilt can let you know everything is ok or that you are forgiven? Is the best remedy. You really shouldn't have to live with it unless for some reason you are unable to contact them or they are dead.
Ask Jesus to forgive you and be the Lord of your life and guide you and give you wisdom about that and all the other things you are facing with relationships. Read II Cor. 5:10; 7:10, Acts 3:19-20, Rev. 3:20, John 1:12-13, II Cor. 5:17.
Do what you think is best then dont worry if someone thinks you didn't do enough. We all do our best if our best is not good enough for someone else then they are expecting more than is reasonable and more than we are willing to do.