According to various pop songs, 'sorry' is one of the hardest words to say. Luckily for Italian speakers, there are a number of ways to say sorry which should make it a little bit easier.
The most basic way of saying sorry is mi dispiace which comes from the verb dispiacere or displease. This phrase has a multitude of roles, but is most commonly used to say 'I'm sorry' or 'I regret'.
For example, mi dispiace per l'inconveniente means 'I'm sorry for the inconvenience'.
A more formal way of expressing sorrow is sono spiacente or simply spiacente which comes from the same root as dispiacere.
Sometimes, even Mi dispiace can sound quite heavy, so if you're apologizing for a minor indiscretion, for example bumping into someone whilst walking, you might say something like mi scusi, scusa or scuasmi which are all equivalents of the English 'excuse me'.
Finally, you could also just skip the sorry part and go straight to asking for forgiveness with *perdonami*which translates into 'pardon me' but can be used in the same way as both 'forgive me' or 'I beg your pardon'.