When trying to say sorry, people often get things horribly wrong by falling foul of insincerity. This makes the person they are apologising to think they don’t really mean it. The best way to say sorry is to be sincere, yet appearing sincere and really meaning your apology takes a certain approach.
Firstly, you need to make sure you at a place in your head where you truly want to apologise. Never apologise out of necessity or when you think you aren’t in the wrong. This will only make you feel like you are compromising your integrity, and the person you are apologising to will know that you don’t really mean it.
Identify exactly what you are sorry for and why you will be making the apology, that way, if the person you are apologising to turns around and says, “sorry for what?” You can reply promptly and sincerely.
Secondly, don’t beat around the bush, being shy, sneaky or coy about your apology. There is a stigma attached to “sucking up” and makes you appear as a naughty child rather than a genuinely sorry adult. Approach the person you are apologising to confidently and directly, pull them aside politely, look them directly in the eye and say the following.
“I want to say I am really sorry. I have thought long and hard about what I did/said, and I realise that it was totally inappropriate/insensitive of me. I hope you can find it in you to forgive me, but if you need time I fully understand and will give you space.”
Of course, the speed and likelihood of forgiveness depends on the severity of the wrong doing. However, this strategy is the best way to say sorry and will no doubt give you the best possible chance of forgiveness.