Allegory wrote:
This question is up there with "How do I make a person like me," in level of relevant information needed to answer the question being provided. You aren't apologizing to some generic individual; you are apologizing to this specific person. Flowers and a card are not going to benefit you at all. You need a specific response that fits this person's needs and the situation. You may be embarrassed about it, but providing us with details will better help us help you.
Here are a few general suggestion:
1. Is this person angry at you or simply hurt? This is a question of whether they need space right now or not, whether you being around them right now is going to make things worse or not. If they don't even feel like talking to you then forcing your apology on them is going to aggravate the situation.
2. Is this person fully aware of your regret or are they not? Answering this question allows you decide on a course of action. If they already know how sorry you are then saying so again is wasteful, you should begin trying to make it up to them (by say taking them some place they enjoy). If they are not aware that you regret what you have done then you should rectify that immediately. If you do not then they will feel as if you do not care and do not feel you have wronged them.
3. Avoid monetary compensation for emotional damages. Simply buying them something usually sends the message you care more about them not being angry with you than how they actually feel. Possibly courses of actions could be simply doing something they really enjoy (For one time infractions), or discussing the issue so they feel you are trying to never make such a mistake again (for usually recurring problems).
Going along with the bolded statement, do you regret that you did it or that you were caught? In other words, with hindsight being 20/20, would you, could you ever make that mistake again?