Don't continuously tell them you're sorry over and over, every time you talk. I know I'm guilty of this myself and I'm trying to stop. Give them time to take your apology into account. Don't go into it expecting them to forgive you. Especially, don't ask or beg them to forgive you. That makes it clear that you're apologizing to make yourself feel better, not them. And most of all, don't apologize if you don't mean it.