This explains the commonly used ways of showing each eye the different image that's necessary for 3D.
- Anaglyphic: Colored glasses (e.g. one red lens, one cyan) are used to separate the image into color channels. Has obvious limitations, such as being unable to handle full-color images well. On the other hand, it can be used easily adapted to other media such as television or print. One variation, ColorCode 3D, uses yellow and blue lenses, and another, TrioScopics 3D, uses green and magenta lenses.
- Polarized light: Depends on light whose waves vibrate in different directions; two such images are projected and each eye is covered with a polarized filter that only lets one image through. Polarization isn't visible to the eye, so this allows full-spectrum color and is how nearly all modern 3D movies are done. Older films used linear polarization, which required the viewer to keep their eyes roughly level to perceive the 3D effect; newer films use circular polarization (clockwise and counterclockwise), clockwise vs counterclockwise "Real D Cinema", which can be viewed at any angle, even if you tilt your head.
- The Pulfrich Effect: Carl Pulfrich discovered in 1922 that it takes the brain longer to process a darker image. An eye with a dark filter (like sunglasses) on it will see a different image than an uncovered eye because it's seeing the image from a moment ago. The two images combine into 3D... if the scene is moving and spinning in such a way that it works out, which limits the effect to novelty films. One example is the non-canon Doctor Who/EastEnders Children in Need crossover "Dimensions in Time"; to see it in 3D, just hold sunglasses over one eye.
- Field Sequential 3D: This works on televisions and depends on having special electronic shutter glasses that alternate each lens between light and dark, synchronized to the TV set's own refresh rate as it alternates between each frame. This can provide full color 3D, but tends to flicker. For a long time, this was only used for gimmicks. Peripherals for the Nintendo Family Computer and the Sega Master System used this sort of idea. There was also VHD, an obscure Japanese video disk format from 1990, which had most of the 1980s 3D movies, and is a common source of 3D bootlegs. Recently, advances in technology have lead to a resurgence for this 3D format. Modern LCD TVs which can refresh several times faster than old tube models have eliminated the flickering and there is a new (backwards-compatible) 3D extension to Blu-ray to provide 3D content in high definition.
- Autostereoscopy: Uses a lensed surface to magnify and project portions of the image in slightly different directions, so that the viewer's eyes see differing images as a result. This can create a full-color 3D effect without the need for any special viewing glasses, but it has an extremely limited field-of-view and thus works well only in small sizes. An electronic variation of the principle has seen some success in Japan with handheld 3D phones, and is also used in the Nintendo 3DS. You may also recognize the technology as the same one used in "3D action cards" (you know, those things with the flickery images that shifted from one frame to another if you tilted them).
- Spectral Comb: The left and right images are sliced up in wavelength by a fine "comb" filter that lets through a bunch of different red wavelengths, a bunch of different green wavelengths, a bunch of different blue wavelengths, etc. The particular wavelengths for the left and right eyes are interleaved, so they don't overlap. Specially tuned interference filters in a pair of glasses filter out the appropriate combs of the spectrum depending on what eye they cover. Each eye receives 50% of the light, but it's spread out amongst all the colours, so you get the effect of a full colour image. Also known as Dolby 3D.
If you wish to know about the act of shooting 3D pictures, read this page