The most common phrase in german phrase book for apology would be
es tut mir leid or
tut mir leid to mean "it does me suffering".
From the questions on the difference between "entschuldigen" or "Entschuldigung"
- What is the difference between Entschuldigen and Entschuldigung?
- Kann man "sich entschuldigen" oder nur "um Entschuldigung bitten"?
it remains unclear when to use which.
How do you use apology towards specific situations? e.g. "I am sorry for my late reply." in emails or "I am sorry, the person you've just asked for is not available"