You are ALREADY in that dimension. You exist in all dimensions. It is only your perception that reduces you to a 3d world.
In order to "see" 4D, then you would need a change in perspective.
For example, science and quantum physics has shown that electrons are not really particals. Instead, they are waves of possibilities, and when viewed they are reduced to a single particle. But it only does this in the presence of DNA. This is known as the observer effect.
As such, the other dimensions are already going on around you, you just aren't aware of them.
As odd as it may sound, the universe would seem chaotic without it. Instead of you seeing just 1 keyboard you are typing with, you would instead see a keyboard in every possible place it could be. Along with everything else in the room/universe etc. On a 4d level, it would be less, but the higher in dimensions you went, the more places that object would be, until you reached the highest dimension in which it would be everywhere. But the wierdness here is that if the universe is infinite, then you would actually just keep on filling in new areas with that same bit.
In effect, you would be able to see inside 3d objects because those particals would be everywhere. Much like the 3d object can see into the 2d safe in flatland. Although near impossible for us to imagine, much like it was for the 2d flatland people.
But your DNA and the observer effect turns that chaos into what you see. It provides a logical path and turns everything into a singularity.
I personally view the black hole at the center of the galaxy as 1 very huge EYE. As it turns everything into a singularity. And when you think about it, that is also what the eye does. Turns those waves of probability into a single particle.
The coolness comes if you can dip into the 4th dimension perception and then come back to 3d reality. And then you can do things like teleport objects(as you will see all the possibilites, and pick the one in front of you rather than the one across the room), telepathy, as you will be able to choose the brain waves of the person across from you, rather than your own and so on.
But then again, maybe you don't need to really see the other possibility, just know it's there to make it work.