"I apologise for missing your italki class" – 'I apologise' is a good one to use when writing, it has a slightly more serious and sincere flavour "I'm sorry / sorry" – is your go to 90% of the time, 'sorry about the mess [in my room]' "Excuse me" is for situations where you interrupt the other persons time or space. 'excuse me' (if you tread on someone's toe) 'excuse me... do you have the time' (stopping someone on the street) This is more of a general guide, as you get more experienced you'll better understand the nuances.

15 down vote accepted Sorry expresses more regret than excuse me does. If I'm trying to leave the room and you're in my way, I'll say "Excuse me." I recognize that I'm inconveniencing you by asking you to move, but the inconvenience is very small, and I don't expect you to be offended by the request. People often say "excuse me" when they commit small violations of etiquette, such as sneezing loudly. If I accidentally step on your toe while I'm trying to get to the door, I'll say "I'm sorry!" I didn't mean to step on your toe, and I regret injuring you.