Oh dear, you've screwed up big time and now you don't know what.
On TV they always send flowers, so maybe that's what you'll do.
But what to send? In order to make the right impression I have two tips for you.
Firstly, send the offended party their favorite flowers.
Doing this shows that you know the person and pay attention to their likes and dislikes, and that you care about these preferences.
If the person you've hurt hates carnations, don't send a bouquet of pink ones just because they were on sale.
You may be thinking, "Hey, at least I tried" but the hurt party will most likely be even more offended, thinking you didn't know them at all.
Secondly, learn about the meanings of the flowers you are sending.
For example, did you know that striped carnations mean "I'm sorry, but I can't be in a relationship with you"? This is definitely not the message you want to send! Purple hyacinths are a good choice, their message is simply "I'm sorry".
Depending on the manner of your transgression you can also send flowers with other meanings, such as primrose which means "I can't live without you", or a blue violet which means "I'll always be true".
The thoughtfulness behind putting together the right message for your bouquet will shine through to the person you are apologizing to.
Saying "I'm sorry" is never an easy task, but flowers can help to ease the pain of such a difficult task.
Good luck, and hopefully all broken ties will soon be mended.