This was the first time I saw the movie Interstellar, and I have to say I am completely blown away. It's easily one of the best movies I've ever seen, if not -the- best. The story behind the movie was just as entertaining as the physics. The movie introduced concepts to the public that few had ever considered possible and did it in a way that was scientifically accurate and believable. Perhaps chief among these and one of the highlights of the movie was the wormhole placed near Saturn by beings from a place with four spatial dimensions, who can apparently warp spacetime with "relative" ease (Eh? Get it? Relative?). Bad jokes aside, the concept of a wormhole is quite simple actually and is depicted very well in the movie itself with one of the characters folding a piece of paper in two and then sticking a pen through it to illustrate traveling from one spot to another over a great distance in a short time. The wormhole in question takes the crew to another galaxy with planets orbiting a black hole. Now, I'm not a rocket scientist (yet), but I'm pretty sure fixing Earth is probably easier than getting Earth's entire population into a massive ship, sending that ship to Saturn and then through a wormhole to another galaxy where the habitable planets are orbiting an enormous black hole named Gargantua. Personally, I would stay as far away from black holes as possible.
According to Kip Thorne, a wormhole is unnatural in our universe with our laws of physics, but for an "ultra-advanced" civilization from a higher dimension, it would probably be a cake-walk. The idea behind a wormhole is that it would require negative energy to remain stable and we have absolutely no concept of what negative energy might be or how to use it. For us, creating and stabilizing wormholes may be stuck in the realm of impossibility with laws of physics.
However if we were to indulge this theoretical idea, how would a wormhole look? Well the odds are it would be a sphere, and light traveling through it from the other side would come through, giving you a picture of what is on the other side. So if there were a planet on the other side, you would see that planet looking through the wormhole. The same goes for the opposite, if there were someone on the other side of the wormhole looking back through, they would see you looking at them.
One theory is that wormholes do actually exist, but they're on the subatomic level, a part of the theoretical "quantum foam." These wormholes are not visible to the human eye and would only be about a Planck Length long. Suffice to say, you won't be going anywhere fast with those wormholes.
The very idea of wormholes is strange in itself, but theoretically they could exist as an alternative to faster-than-light travel. Obviously there are no wormholes simply hanging around Saturn, and we really can't travel through subatomic wormholes on the off chance that they actually exist. So I suppose we'll just have to wait until a group of beings from a higher dimension place one for us to use. In the meantime, we'll continue trying to figure out how to create them anyway.