There are several expressions used in English to offer an apology, like "I'm sorry", "I beg your pardon", "I must apologise". Here are some links to learn more about it.
First connect to the BBC Flatmates series. Listen to the episode first, then go to the Language point and finally take the quiz:
http://www.bbc.co.uk/worldservice/learningenglish/flatmates/episode102/index.shtml
You can also see an episode from "Everybody Loves Raymond" which shows a situation where apologising is not so easy...
https://www.youtube.com/watch?v=YfZJpu34maw
Another apologising situation from the show "Friends"
https://www.youtube.com/watch?v=bIIm7yBdUG4
Enjoy!