For starters, he should fight with the mentality that there is always a chance that his opponent could see reason and alter his life. Not even his parents or Lois being kidnapped by his adversary should alter this belief in him.
Also, no one in any of these films should ever have to talk Kal down from "going too far". Ever. His respect for life should trump any and every emotion that flows through his veins. So Goyer and Snyder, I don't want to see any moments where Kal speeds home to have a "talk" with Ma and Pa Kent. Nor does he need one from Lois, ever. I've seen enough of this nonsense in "Smallville".
Now with that said.. the basics:
- In a fight, Kal should be more cunning than he is intelligent. No matter who he faces, he should be the least experienced in combat, which should constantly give his opponent an edge to begin.
- There are two advantages that not only he, but everyone in the galaxy should come to the understand when facing him:
1. When on Earth, his fighting awareness is second to none. So good should they be, that quite a few of his battles against aliens should be won just by the fact that he knows his surroundings better than them. This should make him feared.
2. His fighting spirit should be the greatest of any hero, never quitting or surrendering no matter how bleak the situation is. The vast amount of time and energy that it takes to defeat him should be enough of a concern to keep most beings from coming to Earth to challenge him. This should make him respected.
Now, how he should fight:
* When facing a normal human he should never use any use heat vision, freeze breath, and especially a punch or a kick. A toss is acceptable but only when he aims the criminal toward a place that provides some cushion such as a crowd of other crooks, a watery surface, or a dumpster with necessary cushion inside; never through a window or some hard surface. Roughing up a thug should be avoided at all costs so that he won't be looked at negatively as a bully.
And after saying all this, one of the wonderful things about Superman is that a simple tap on the window and a wiggle of his finger is all that's needed 9 times out 10 for a criminal to willingly give himself up. That's if the movie does it's job in showing the full scope of what Superman represents to the criminal world.
* When facing a former friend/ally, a metahuman, or your basic alien with powers he should fight not to lose. His fighting stance should be one of defense, delivering the occasion offensive maneuver to keep the opponent honest. His legs spread to the width of the shoulders, posture slightly leaning forward, arms raised, senses on high alert. Gentle words should be his greatest ally, always attempting to get through to the person and calm their rage.
This should go on until Kal's or bystanders' lives are in danger. Then a combination of moves should be delivered to end the fight; sparing as much damage as possible.
* Against an alpha-enemy that he knows is killing or will kill without regard, he should fight to win; using the full scope of his powers. His stance should be lower, his knees bent, and eyes ablaze. His fighting type should be "brawler/roughneck", much like a strapping Kansas boy would fight in a bar. Shoulder charges, hay-makers, kicks to gut, face slamming to hard surfaces, arm tosses, suplexes, elbows to the front and the back, and never allowing himself to be on the ground when an opponent is near.
Not until the opponent is fully defeated should he hold back. At that point, he ends the fights and sends them back where they came from.