Conditioning is important, but not integral for being able to punch hard.

The most important thing is to be in a position that gives you leverage and gets you set for a punch. Learn how to shift your weight from one leg to another, how to use footwork to add power to your punches. What goes hand in hand with footwork is the different shifts/sleights, with a simple step, pivot, and adjustment to your stance you can evade punches while simulateosly add power to your punches. I'll go over them in detail later on. In light of that the best way to improve your punching power is to use a mirror. Why a mirror, because it's the best way in seeing what you're doing and make adjustments, you can study the various feints, shifts, set-ups while you are shadowboxing in front of a mirror.

As for physical exercise you need to be explosive on your feet. I think skipping rope is a great way to achieve that. There are many different exercises that can make a jumprope much more intense.

As for muscles are concerned don't get carried away on a weight training pallete, what's important is that your training is result orientated. Focus on the muscles that you'll be using.

It's important that you strengthen your back, your abs (including the obliques), your legs, and body as a whole. There are many exercises that are worth looking into: plyometrics, isometrics as final supplement, certain weight-training, manual labor, or hard physical activities.

Improving your power is worthwhile, but shouldn't be center focus for your training, technique is important, and more important is the reason behind those techniques. You can only hit as hard as the best punch you can land. Do things in your head, always have a reason while you are training, imagine slipping their lead, side-stepping away from their rear arm, while simulataneosly shifting to deliver a terrific punch!

Now guy's like Marciano, Tyson, Dempsey and countless others were not mindless punchers. Rocky Marciano didn't look pretty, but he knew how feint, and set up his punches. Tyson was a counterpuncher in his hayday, he'd look to slip their lead and attack their weaker angles.

Show me a hard puncher without reasons behind what he's doing, and I'll show you a dead man.