Basics / Cameras
Just like humans naturally are seeing their environment with two eyes, the basics for any stereoscopic 3D photo are two images. Those images have to be taken ideally with about human eye distance (stereoscopic base) - so between 6 and 7 cm.
Stereoscopic 3D is no brand-new technology. Since a very long time, stereoscopic photographs are produced. Ups and downs of this technology mostly are depending on easy viewing capabilities for a mass market. In former times viewing stereoscopic content was extremely cumbersome.
Today, the technical progress set the basis for stereoscopic 3D to become a mass phenomenon. Since 2010 almost no TV was announced that does not also have 3D viewing capability.
Orientation of stereoscopic 3D images
Orientation technically is the computation of the exact position/distance and rotation of the cameras for the left and right image. Accroding to the angles of the cameras, a rectified image projected to a planar surface is created. These two rectified images are then mounted into a stereoscopic image format like side-by-side or anaglyphs. A good and free utility for doing that is the Stereophotomaker.
Viewing stereoscopic 3D content
Foremost well-known are so-called anaglyphs. In this case the right image is overlayed over the left image while both images are separated by a coloured filter (e.g. red and cyan). To view anaglyphs, glasses have to be worn that have exactly the same filter colours for the left and right eye.
The advantage of this technique is the simplicity and the low effort. Drawback, however, is that colours are no longer exactly preserved as there will be colour casts.
Also well-known are lenticular images - typically found for 3D post-cards. Here, the separation for the left and right image will be done with a interlaced prism cover on top of the post-card. Interlacing means splitting the stereoscopic into vertical columns altering left-right-left-right etc.
The advantage is that colours are fully preserved and viewing the 3D image does not require any special glasses or VR devices. Disadvantage is that the price to create lenticulars is still relatively high.
There are also other methods like KMQ viewers that I won't explain in detail here. If you are interested, see the Wikipedia articles on that.
New modern methods at reasonable prices are available now on TVs and computers either with polarization glasses or active shutter glasses. For shutter glasses, the monitor has to be able to support at least 120Hz refresh rate to guarantee a flicker-free experience - that means that changing from left to right image and back is done at a speed that our brain does no longer recognize. The shutter glasses are synced with the monitor so the right eye will only be "open" when the right image is displayed. Shutter glasses are active glasses which means they require batteries.
Polarization is passive, not requiring any batteries. In this case, on a monitor there is a polarizing pattern installed which passes through polarized light separated for left and right eye. The polarization glasses have the corresponding filters to receive the left or right content, only. Typically the pattern is an interlaced altering left-right-left-right... horizontal split of the images - best to be viewed with 4K monitors ( I am using a 4K 3D-TV from Phillips for example).
Research is still done on lenticular monitors that don't require any further glasses. But that is still in early stages.
For more detailed explanation you are welcome to follow the links on my web-site to Wikipedia or manufacturers and organizations.
Deutsche Gesellschaft für Stereoskopie e.V. tips and tricks, information about events and groups
International Stereoscopic Union (engl.) the only international society for 3D and stereoscopy
Stereophotomaker free tool for orientation and visualization of 3D content.
Nvidia 3D vision information about 3D hardware, pc, tv...
Fujifilm Real 3D small 3D camera and lenticular monitors