An apology has three parts:
(1) "I'm sorry",
(2) "Here's what I did wrong", and
(3) "Here's how I'll make it better."
The first two parts of a proper apology are closely related, so we'll deal with them together. Some people find "I'm sorry" to be the hardest phrase to say. To an extent, they're right. It's never easy owning up when we've done wrong. That's still no excuse to hide from guilt - because that's what you're doing when you refuse to admit you've done wrong. You're hiding. Coward.
You're hiding from those who know you've done wrong. You're also hiding from yourself. Fast and far as you may run, your guilt will be right on your heels everywhere you go. Keep running if you like, it won't do you any good. Run coward, run. Watching you squirm is more fun than you ever will know.
Some people feel they never have to admit they're wrong. Still others blurt an "Oops, sorry" as to sweep their actions under the rug when they know they're in the wrong - like the guy who gives you a facetious "Sorry" after his SUV rear-ends you because he was yakking away on his cell phone while driving.
Both of these types reek of entitlement. We have no patience for either of them, and frankly, they make the bile surge up into our throats. We're not ones to advocate violence, but if people like these were gagged with a shovel on a pubic street, we wouldn't look the other way. We'd stretch out on lawn chairs and watch.
The final part of an apology is making things right. Note: do not try to make things right without admitting what you did wrong - you will come off as a bigger douche.
Ever hear the expression "bury the hatchet"? It's an old phrase synonymous with making amends with someone. Burying the hatchet implies forgetting where you placed it, or else you might dig it up again and bury it in someone's head.
When you make an apology, you'd better make it count. Bury that hatchet forever, because there's a word for when you've buried the hatchet and you later show up with it in your hand. It's ambush. You can do this to someone only once.
If you opt for the ambush tactic, don't expect another apology to smooth things over. In fact, this is the fastest way to win enemies. Make the most of that hatchet you dug up, because whoever you plan to use it against may already be planning to burn your house down - and if you've really ticked him off, he'll burn it down with you in it, when you least expect. Ambushes are a bitch, aren't they?
Be nice. Or else.