What are the basics of 3 dimentional projection?

Maybe this is just a term that I don't know, but it sounds like you're
asking something more like one of these:

What are the details on how light from 3-dimensional space is cast on
a two-dimensional optical element, such as a camera?

How do I produce and insert CGI into a movie I'm recording?

How might I create or use a device that produces a 3-dimensional image?

How do I create a 3-dimensional-projection special effect in a film? 
(Like a holographic-telephone in a sci-fi movie)

I am going to assume that your question differed from the first post's
answer, meaning that you wish to know how to physically project an
image in 3D space.  One of the first problems with this is that light,
in order for you to be able to see it, has to either come from an
object (projector) or be bounced off one (film screen) before it hits
your eyes and is resolved as an image.
There are mulitple techniques to accomplish a "fake" 3D image: 
Spinning a lightsource or screen at a high velocity to make the
spinning object itself seem invisible, and any light it generates or
reflects appears to be "floating" with the bonus that you can walk
around it.  You will, however, see the same image no matter what
angle, unless the device can sense your position change, and change
the image to suit you, or the device is programmed to change what
"slice" of the image it generates for each degree of turn, many many
times a second.
The second way, seen on SeaQuest DSV, was to have a "fog screen"
blowing from bottom to top or top to bottom, and a flat image
projected on it from a hidden projector.  While not true 3D, it gives
the appearance of an image or video to be floating in mid air, but the
image is not steady due to the chaotic nature of fog.
At the present time, we do not know how to make photons either
generate in mid air with no apparent source, or be reflected in mid
air with no apparent reflectors.