Start by finding a quiet area in your house where you can address your sister in private. This may be in a room you share together or in your sister's room. Making the apology in a private, quiet space will show your sister that you are serious about your apology and want to discuss the matter away from others. Try to make your heartfelt apology in person, face to face. Texting or emailing an apology can seem disingenuous and may not hold as much of an emotional impact as an in person apology. You should also choose a time that is most convenient for your older sister. Do not try to apologize to her when she is in a rush and on her way out or when she is hanging out with friends at home. Choose a time where she is alone and can focus on your apology. Begin your apology by noting that you hurt your sister and that you want to address her hurt feelings. Do not use "if" or "but" when you speak to your sister. Be honest and acknowledge that your sister is upset. For example, you may say, "I understand that your feelings may have been hurt when I read your diary without asking for your permission," or you may say, "I realize that I made you upset when I said unkind things to you in front of your friends." You should then be willing to admit that you acted poorly or that you were in the wrong. Taking responsibility for your actions will show your sister that you realize you behaved badly and want to make amends for your behavior towards her. Avoid mentioning your sibling's own behavior and do not try to blame your sister or make her feel bad. You are apologizing for your actions, not putting your sister on trial for her actions. Blaming her will only make her more upset. You may say, "I know that I acted badly when I read your diary" or "I can see now that my unkind words toward you were hurtful and unfair." You may also say, "I was mad at you but I should not have taken my anger out on you." Make sure you own up to your actions by using "I" statements in your apology. This will show your sister that you are standing by your words and willing to acknowledge that you acted poorly towards her. You should say "sorry" once to your sister, with intention and feeling. Avoid saying "sorry" multiple times as it may sound hollow or empty after you say it once. Maintain eye contact with her when you make your apology. This will let her know you are serious and genuine. For example, you may say, "I'm sorry for what I did to you," or "I apologize for being hurtful and unfair toward you." Do not expect your sister to forgive you right away. She may accept your apology but still be upset at you, or she may not respond at all to your apology. Your sister may need time to process her anger and will accept your apology when she is ready. Keep in mind your sister is not obligated to accept your apology right away, or at all. You should be respectful toward her and give her time to forgive you. If your sister responds to your apology with feedback or comments about your behavior, you should listen to it without judgement. Be willing to listen to what she has to say and use this feedback to improve your behavior towards her in the future. Do not retaliate or get upset if she responds to your apology with comments or feedback.

Summary:
Find a quiet, private setting. Acknowledge your sister's feelings. Take responsibility for your actions. Use "I" statements in your apology. Give your sister time to accept your apology.