So I've been experimenting with stereo photography the last couple of days. I think I've got it down.
In the old days they used a single camera with two lenses that could take two slightly different views of the same scene, simultaneously. When combined on a card and placed in a special viewer the images would merge and create a three dimensional effect. The brain would do what it does naturally and interpret the angular differences between the two pictures as depth.
I just have the one camera, though, so I have to choose subjects that are perfectly still; no wind blown objects, falling snow, fast moving clouds, etc. I take one picture, then immediately move slightly to the right and take the same picture again being careful to frame the second photo with the same landmarks as the first. In Photoshop I combine the two images into a single picture with the left and right images next to each other.
Now admittedly it is far easier to get a three dimensional effect with a viewer, but few people have them lying around anymore. However I've found that it's possible to see a 3D image without a viewer if you don't mind going cross eyed. This takes a little practice, and it tends to give you a headache if you stare too long, but here goes...
Look at the image and let your eyes relax a little. You'll notice when you do that the two images will tend to drift together. Use this natural drift to your advantage and force the images to keep drifting until they seem to overlap and combine to form a third image in the middle of two fainter peripheral images (it may be helpful to back away from your screen so your eyes don't have to cross quite as much).
Once you've aligned the two images into the third you should begin to see depth of field. It's a bit difficult at first to hold the image, and again it may help if you back away a bit. Once the image is captured, slowly move closer to your screen while holding the image together to experience more detail.
The following is a demonstration of what you will see as you combine the two pictures together. This is a flat interpretation. The actual images tend to shimmer around the edges when you do it for real. This is due to your brain not getting quite enough information in the periphery to make sense of what it's seeing.