I agree with Scrap that everybody is a counter puncher- you have to have an opening to land effectively and, every time a punch is thrown, an opening is created. A very simple and pure counter punch is the straight right to the heart under a left lead.
To me a key ingredient to being a good counter puncher is being fearless, and this comes from mastering the skills of slipping, parrying. Blocking ties up your hands and you can't punch back. You need to be able to make your opponent miss by the barest of margins and punch back in the same motion.
And the techniques of boxing lend themselves to this- for example, slipping a jab over the right shoulder is essentially the same as throwing a right hand.