Don't hesitate when you know you're wrong. Just set aside your pride and apologize. The longer you wait, the harder actually saying the words becomes. Plus, he's going to feel even more slighted if he has to wait days for you to admit you were wrong. After all, if he owed you an apology, you would definitely want it sooner rather than later.
If words alone won't prove that you really are sorry, sweeten the deal. Offer to take him out to dinner or a movie of his choosing; better yet, surprise him with one of his favorite treats as a peace offering -- for example, bake him some cookies, stock the fridge with his beer of choice or do a chore that he hates.
Don't expect everything to be OK immediately after apologizing. Depending on what you did or how much you upset him, he may need some time to cool off and let your apology sink in. Tell him you understand he may need some time, so you're going to give him some space. Leave the room or go for a walk so you're not tempted to start another argument about why he hasn't forgiven you yet. If he drags it out, you can discuss, but if he just needs a bit of time to himself, just let him be.
An argument every now and again is good for your relationship but staying mad over something petty will only hinder the situation more. Often, the best things you can do are recognize when it's your turn to say your sorry and be ready to move on.
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