During Man of Steel, Superman battles and defeats several military trained Kryptonians (eg. Zod, Faora etc) who have much more training and combat skill at their disposal. Faora mentions that he is weak and unsure of himself and Zod mentions that he has trained his entire life.
So how is Superman able to defeat them, is this explained/hinted at in the movie at any point?
He is able to do this because in this version of Superman he was born not cloned (that part has nothing to with his power set) and the codex was infused into his body. The codex is every Kryptonian that has ever lived or will ever live. He is literally ALL that ever was or ever will be of Krypton. He has access to all of the information stored in each cell by the codex and that's why he is so powerful.
And yes, he has been on earth for far longer and is far more powerful than any of them would ever be! He was in the literal sense made better than any other person from his home world.
Clark has been on Earth his entire life and has become very familiar with his super-powers and with the atmosphere. The Kryptonians have not and although they might seem to have become used to their environment incredibly quickly, they haven't.
At several points Zod is shown attempting to get used to his powers. As an example, he has problems controlling his ability to see through things. We can imagine this extends to the rest of the Superman abilities.
This lack of experience gives Superman the edge. Plus the Kryptonians are some what handicapped because Clark is/contains the DNA of their species. So they can't just do whatever they please, they have to be conscious of preserving him.
They actually said in the film how the atmosphere of Earth is more nourishing, and the sun provides him with more energy. This happened over his entire life, and only a short while for the other Kryptonians, therefore Superman has essentially had a great diet his whole life, whereas the Kryptonians have been eating junk food: he is physically in far better shape.
Acquiring the power of Superman would make all other training irrelevant. Consider Judo, which uses gravity to facilitate falls. You can't trip someone who can fly, no matter how many belts you have. The best boxer in the world would be just as mowed down by a machine gun as a couch potato would be. Also, Brandon Routh's Superman took a bullet in the eye and didn't blink, so even vulnerable spots on a non-super become insignificant at Superman levels of powers.
At that level of power, the power level is the only significant thing, barring (in this case) access to Kryptonite. As others have mentioned, Superman has higher power levels than does Zod due to his longer exposure to the Sun and the Earth's atmosphere. Superman, therefore, wins through power-imbalance attrition, as is shown in the movie.
I think the answer talking about Clark being more used to his powers is right, and Zod etc do have trouble with them.
BUT the codex bit is totally wrong, as the scientist on Zod's ship says he doesn't need to be alive to harvest the codex from his body.
The way Superman can defeat them is having more experience with his powers, coupled with having been on Earth longer, so his cells have bathed in the radiation of the sun longer; he has become stronger through that.
Think of two boxers preparing for a fight. One has been exercising his entire life and learned to box later on life while the other has been boxing his entire life. The first lives in high altitude while the second lives in lower altitude. They end up fighting at high altitude where the first is accustomed to while the second has troubles.
Superman is the first guy, Zod is the second.
This has been mostly answered, but I'll repeat it and add another insight.
A) As others have said, he's been soaking up our Sun for way longer. Thus, he's more adapted to the powers that come with.
B) The only reason it even seemed close was the Kal-el really didn't want to kill the last remaining kyptonian. The other militants were in the phantom zone and really, Zod was the last of his kind. After growing up in a world where he had to walk on eggshells his entire life and would inevitably face fear and criticism, having one other being to share the existence with would've been a sweet dream. Much more, the last survivor of your race and your home. But in the end, he is forced to choose between his race (Zod) and his people (Earth). He always had that choice, but Zod forced his hand one way. So Superman used the power he always had and ended it right there. That's why he screams mournfully right after.
