An apology serves three purposes. First, it claims responsibility for past mistakes. Second, it announces your commitment to change and, third, it works as an agreement between both parties. When you apologize, say the words, "I'm sorry. I'll try to do better." Then say nothing else. Do not qualify your behavior or make excuses for your actions.
Just saying you're sorry for past behavior is not enough. You must announce loudly and clearly, again and again, that you are committed to making a change. This personal advertising help you change other people's perceptions of your behavior and it holds you accountable. It also gives people permission to monitor your progress and offer suggestions.