Excuse me! and I'm sorry!
In English, we use "excuse me" and "I'm sorry" for a variety of situations. Por ejemplo, you bump into someone at the grocery and you say, "Oh, I'm sorry!" Or you need to pass through a group of people and you say, "Excuse me!" Or you do something wrong and you say, "I'm sorry!"
In Spanish, there are a few ways to say this.
1. permiso (say pEHr mEE soh)
2. disculpe (say dEEs cOOl pEH)
3. perdón (say pEHr dOHn)
4. lo siento (say lOH see EHn tOH)
Permiso is used when you need to pass through the aforementioned group of people. Or when the lady at the grocery parked her cart in the middle of aisle and is taking her sweet time reading the labels on every package of beans on the shelf.
Disculpe and perdón and lo siento are all used to apologize. You could use any of these if, when you got tired of waiting for the lady and she ignored your permiso, you bumped her cart to let her know you were serious. It is then that you apologize with disculpe/perdón so she won't know you did it on purpose. ;)
I should add that lo siento is used for more of a heartfelt apology, as in, you were in a really bad mood yesterday and were mean to your hubby. ;) Or when someone tells you that their friend/relative died, lo siento is the only appropriate form of "I'm sorry" to use.