There is a reason Superman is called "super". He has super-strength and super-speed. He flies, and he is mostly indestructible. He can shoot laser-like things from his eyes. Finally, he has some type of X-ray vision. Although comic book scholars have debated Superman's vision before, let's consider how it could work.
There is one important aspect of human vision. In order to see an object, light has to go from that object to the eye (light in the visible spectrum). The light from that object can be either reflected light or the object can emit its own light. But either way, the direction of this light is from the object to the eye. This is important.
The eye is only a receiver of light---there isn't some type of "vision ray" that shoots from the eye. I only point this out because it's actually an idea that some people have about light. Ask yourself this question:
The answer is that you will see black and nothing but black. Black is the color our brains associate with the lack of light. However, many people will give an answer that you will some some stuff after your eyes adjust. Perhaps their answer is based on their previous experiences (you rarely get an absolutely dark room) but also on their idea that the eyes do the seeing and can adjust to new situations.
We can make X-ray images. That's not science fiction. Here's how it works. If you take high speed electrons and shoot them at a metal surfaces, you can produce X-rays. X-rays are just like visible light except they have a much shorter wavelength (but they are still electromagnetic waves). But since X-rays have a different wavelength (and frequency) they interact with matter differently than visible light. This means that some materials (like human flesh) are partially transparent. You can use this to create an X-ray image by shining X-rays through a human and putting an X-ray detector on the other side. The X-rays don't pass through bones as much as flesh, so you can get an image.
So, how could this work with Superman's vision? If his eyes could detect X-rays like humans detect visible light, he would still need an X-ray source. Could these same X-rays come out of his eyes (or other parts of his body)? Sure, but in that case he would be detecting X-rays that are deflected from these human tissues, not the ones that pass through. I'm going to guess the intensity would be a bit lower. Anyway, this would be the human equivalent of having flashing lights in your eyes.
But aren't there natural sources of X-ray radiation? Yes, there is an X-ray background radiation---cosmic X-rays. However, the intensity is so small it could hardly be useful for superheroes.
What if Superman could see into a human body like the MRI does? I guess the first question that comes up is "how does an MRI even work?" MRI stands for Magnetic Resonance Imaging. It's pretty complicated---but I will try to give my Haiku-level explanation.
A proton (like the one in a hydrogen atom) acts like a tiny magnet because of nuclear spin. When you apply a super large magnetic field, these protons will have their "magnetic poles" (quotes because that's not really what it's called) align with this field. The protons can be excited to higher energy states by applying another external radio frequency---but when they relax back to their lower energy, they emit radiation. The MRI then detects this radiation and uses it to make a 3-D map of where all the hydrogen is in the body. Different tissues have different amounts of water---so different amounts of hydrogen. That's about as short of an explanation that I can make.
There are two key points to the MRI if it were to be adapted as super-vision. First, you need a large magnetic field---super large. Second, an MRI image isn't created all at once---instead, it takes time to vary the magnetic field, detect different signals and finally use algorithms to process the data into an image. The only way to make this work with Superman would be to very rapidly move around an object to observe the radiation at different locations all at the same time he is creating large magnetic fields. No, it wouldn't work.
There are some other ways that Superman could see more than a normal human. What if he could see in the infrared region? That would be just like using one of the thermal cameras (which you should play with if you get a chance). Sure, you can't really see the insides of a human with infrared but you can see some really cool stuff (and you can see through some things). The same could be true for ultraviolet light. Not only would you see different details in UV light, but there is already plenty of it around---especially if you are outside.
You know what would be fun? What if Superman could see cell phone signals? This type of radiation is just about everywhere on the surface of the Earth (yes, I know---it's everywhere except in your bedroom where you can never get a good signal). Also, this frequency of radiation can "see through" many different materials. Of course, there is one problem---resolution. If you consider cellular data with a frequency of 2000 MHz, this will have a much larger wavelength than visible light (400-800 THz). With such large wavelengths of cellular data, you can't really see very small things. Still, it would be cool.