There are many different ways to individually send an image to each of your eyes. We talk about the different technologies that exist below.
In combination with a pair of powered glasses, these displays work by switching very rapidly between the left and right eye images. The glasses shutter each eye very quickly in tandem with the screen so that only the correct image is seen by each eye. So while your regular TV might refresh 60 times per second at maximum, a 3D TV would have to refresh at 120Hz in order to get 60 frames per second to each of your eyes.
If you are looking at the current crop of 3D TV’s, then you’re going to end up with an active shutter device. Why is this? I’ll explain in more detail later, but in essence active shutter displays are the cheapest way right now to get 3D into the home.
One point of confusion that we need to clear up here is that just because a TV says it is "120Hz" or "240Hz" does not mean it is 3D capable. Most of these TV's accept only a 60Hz input and do processing to interpolate the frames in between up to 120Hz. If you are buying a truly stereoscopic 3D capable active shutter display, it will be marketed as 3D capable and it will consequently accept a true 120Hz input.
In combination with a cheap pair of polarized glasses, these displays actually display the left and right eye images at the same time. However, the left eye image is polarized in an “opposite” way to the right eye image. The polarizing filter in each lens is then able to let all of the desired image to its eye while blocking out the opposite eye’s image.
In theaters, this is usually accomplished by running two separate projectors with different polarizations. In the home, there are certain types of monitors that accomplish this by alternately polarizing every other row of pixels in a 1-2-1-2 pattern. Unfortunately, as you might guess, this halves the effective resolution of your display while viewing in 3D. I believe full resolution displays of this type also exist, but since twice the pixels are required, no full resolution display for the home has mainstream pricing.
It is actually possible to set up a dual projector rig in the home similar to a 3D setup in theater. However, this requires two projectors to be driven independently and in sync by the same computer. In essence, this approach is very hacky and requires a lot of cooperation between computer, video driver, software and projectors … making it unlikely to work well in more than a few cases.
Anaglyph 3D technology shows both left and right images on the display at the same time, but each eye's image is encoded with a different color mapping. Different color lenses are present in the glasses used to view the image … hence the iconic red and blue glasses … one color for each eye. Newer implementations have used different image coloring, claiming to be superior to the red and blue lenses. This may be true, but in no way does any anaglyph technology hold a candle to the other display technologies mentioned here.
Anaglyph display technology was popular mostly in the 80’s and all the way back to the 50's … mainly because it requires no unusual display technologies at viewing time. Any display can display in anaglyph mode. Due to the state of display technology, this was the public perception of “3D” viewing for a long time. The glasses used for this are also extremely cheap … essentially being just some colored cellophone and cardboard.
Anaglyph technology suffers from severe color distortion and crosstalk between left/right eye images … which can really give you a headache. This technology doesn't even make a pretense at trying to get it "correct" … it just shoots for creating some illusion of depth.
Head mounted displays
These are basically powered glasses or helmet like devices that actually contain a separate display for each eye. While theoretically the least prone to problems, the main problem with these is that they are expensive and displays have not been miniaturized to a usable point. So far only 720p per eye has been achieved and costs run into the thousands. Of course, only one person can use these at a time and doing so is completely anti-social. And, if the head mounted display is not sufficiently miniaturized, it can result head and neck strain for the wearer. But, of all the stereoscopic 3D approaches, it is worth noting that head mounted displays are an approach that can actually create a perfect stereoscopic 3D image for the viewer.
Auto-stereoscopic displays are termed so because they hold the magical promise of being able to show you something stereoscopic 3D without making you wear glasses. Typically, this works because the display literally angles half of its pixels to the left eye and half to the right eye. While this obviates the need for glasses, it also means the effective viewing position is extremely constrained. In practice this limits the number of viewers to one and also cuts the effective resolution of the display in half. As such, auto-stereoscopic displays are more useful in a handheld or certain computing contexts. For example, the Nintendo 3DS is probably going to be the most mainstream example of auto-stereoscopic technology for the next few years.