Forgiveness is completely forgetting something unfortunate that has happened to you and letting go of any grudges or negative feelings toward the person that could have been the cause of that negative situation.
You can't "forgive but never forget" that is just you saying you aren't ready to forgive yet.
Negative situations will result in an emotional scar that is not easy to get rid of, but forgiving and forgetting is the step in the right direction for getting rid of that scar.
How do you forgive the person? Simply put yourself in their shoe, give them the benefit of the doubt, try to reason out why they acted a certain way, and most importantly don't take it personally.
The most person that will benefit from forgiving is you, so why not put that energy that could go towards holding a grudge into forgetting and completely forgiving.
Remember this, forgiveness is a sign of strength.