We see the screen in 2D.
The art or visuals are made so that our brain automatically process the depth by analyzing the size, shading, and view point of the objects on camera.
In 3D movies, they use a little trick in which the brain is tricked into actually thinking something is closer than it really is, making you feel more submersed in the movie or game. This is done using layers of images, with each layer being distanced more or less (which decides its distance). Our eyes perceive distance because there are two of them from different vantage points, which lets our focus be seen from two different directions at once.
The best example of what I'm trying to say: Close ONE of your eyes. You THINK that you still see in 3D (and you do), but your ability to perceive depth just sunk considerably. Take two pencils while having one eye closed, one pencil in each hand.
Now hold them up in the air (about a foot away), with the lead pointing each other like this.
[Image: http://img.photobucket.com/albums/v608/KitaeK27/pencil.png]
Try to make the lead connect each other. You'll find that one of the pencils will be further away from you than the other despite it looking pretty darn close. Its not impossible to put them together, but its MUCH harder compared to doing it with both eyes open.
Thats how 3D works. It takes that very process, but does it for you via screen, which makes things stand out.
4D is nothing but a scam. We cannot perceive 4D, but there are lots of attractions dubbed 4D. These attractions usually make use of the chairs and theater themselves moving to give you a PHYSICAL feel of what you're watching, instead of just a visual one (ie, changing temperature, blowing wind, moving seats, etc).