I think the best way to give a sincere apology is to be upfront, confess of what happened, and then look the person in the eyes and let them know you are truly sorry. Some things can't be passed on with a sorry, but the notion is good nonetheless.
I agree with you, sometimes "sorry" alone isn't enough to forgive someone, but if you see that they are making an effort to make it up to you and that they really do feel bad for what they did, it'll help you forgive them.
I've had many relationships where my significant other would only say "sorry" and though it was nice of them to say sorry, I felt like sometimes they didn't really mean it or they only said it so I wouldn't be upset anymore.
It's healthy in a relationship to always talk things out and understand why someone is feeling the way they are and how, in the future this same situation can be avoided.
Like Ringo said, some things can't be passed on with a sorry.. However by making an effort to show that you care and that you truly are sorry shows that they understand that they made a mistake and they truly are sorry.
I am a person who is more than willing to say sorry a lot of the time because I'm often willing to accept all my own faults and take the blame. Forgiveness of the one I've done wrong by is more important than winning the argument. I admit sometimes I worry about the possibility that I've done something wrong far too often and I end up saying sorry too much and becoming a big annoyance when I desperately want forgiveness and not getting it because the other person is much too annoyed, confused or doesn't think I need to be sorry. I do this with my boyfriend and my parents. All the time.
It feels a bit pathetic.
I'm not this way at school as I'm careful not to make myself into someone vulnerable as I really am.
When I do say sorry though, to people I love, I always sincerely mean it. You can always tell this because the tone in my voice changes to being serious or upset. I never just fling out a sorry in my speech just to fix something. It's because I mean it.
