Everyone makes mistakes. But, not everyone knows how to make an apology. Effectively expressing a sincere apology is a valuable function that will show off your excellent manners. Showing consideration for others is an important part of effective communication. Here are some useful sentences for reference.

General apologies:
Excuse me.
I’m (so/really/terribly) sorry.
I apologize. /My apologies.
I can’t tell you/ You don’t know how sorry I am.

Apologizing for one’s mistake:
I’m sorry for what I’ve done. /I shouldn’t have done that.
How can I make it up to you?
I do beg your pardon for the mistake I’ve made.

Apologizing for bothering someone:
I’m sorry to bother/ disturb/ trouble you.
Sorry, I didn’t mean to bother/ disturb/ trouble you.
I’m afraid I’ve brought you a lot of trouble.
I’m sorry to have caused you so much inconvenience.