I was going to go into a lengthy discussion on how to project astrally (go 'out of body'), but it seems there are now several books available on the market that go into that for me. If you are completely unsure of what to do, then I highly recommend picking up Robert Bruce's book "Astral Dynamics." (available through this site's Books page.). It's also far more in depth than any of the older projection info provided on this website. So long as your energy fields are well developed (through exercises as can be found in Bruce's N.E.W. article), then the projection advice found within older documents on this site will likely be effective.
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Astral projection is simply mental/spiritual travel out of the body to any place on the astral plane; the realm of dreams and spirits etc. It's as easy as daydreaming, but full transfer of consciousness to the point where the experience is more real than normal waking reality takes practice.
The most basic methods for projecting involve closing the eyes, getting into a deeply relaxed state via meditation, and 'believing' that you are in a place. Try to feel that you are actually in a different place from where your body is located. It can be across the room even. Touch the walls with your mental 'body' (just as you would have in a dream), and try to feel them as real.
Believe you are in a place, and you will be there.
Early attempts at projection are often like controlled daydreams, but with practice they become more real and vivid, and contact with the physical realm can even be made and information brought back with accuracy. The biggest problem most people have is that they think there will always be an immediate conscious separation of the body/mind that they will be able to witness right away. When learning to project, try not to pay any attention to your body or the act of separation. Usually, consciousness of the body is never fully lost (you just ignore the body in favor of the vision), and the transfer of consciousness over to the 'vision' or astral landscape is most easily accomplished by allowing it to occur gradually; the more you practice 'seeing' with your mind and traveling with your mind, the more you'll be able to focus your attention on the astral plane, and transfer of consciousness will be gradual and almost unnoticed. This is the easiest way to project. (Note: some people refer to this method as projection of the mental body - projection of the astral/etheric body is far more intense in feeling/perception but some people do it more gradually, whereas others learn to do it instantly. It doesn't matter how you get there so long as you eventually do.) Some people can and do experience a definite separation that occurs everytime, but that is a different method of projecting I won't go into here (Edain McCoy refers to it in her book as chakra projection). The end results of projection are essentially the same, however.
What does a true projection feel like? In the later stages of projecting when you are becoming skilled at it, a full projection usually feels and appears to be even more REAL than regular physical reality. Colors and sounds are far more vivid, and sight is broader in scope (not limited by eyes). In some ways it is like being awake and super-conscious in a dream, but more vivid and real than any normal dream you've ever had.
Hope that helps peak some interest.
More info on Projection taken from my
Real Magick occult forum postings.