To first understand astral projection, you must understand the plane in which you visit. This is the astral plane, to learn more about what it is, check out the 7 Planes of Existence page in the Occult section.
Astral Projection is where your consciousness leaves your physical body to your astral body. Now, this is not a literal leaving, its is more transferring from one body to another in order for it to travel.
Now, you never actually are disconnected from your physical body when you astrally project. You are linked by a silver cord, you may see this, you may not. I personally have never seen it.
Method
Introduction
Unfortunately because I cannot find a good enough universal exercise for astral projection, I will put up my personal one. Now, I cannot guarantee that it will work, because each person is different.
Relaxation
Firstly when doing astral projection, relaxation is a must, because if your body is not relaxed, the physical shell has trouble allowing the astral self to travel.
Find a place where you feel comfortable and are free of distractions, or at least, in a place where it lessens the amount. I also recommend to do this exercise in darkness, as this assists in your concentration and projection.
Sit, lay or get in a position where you can stay for long periods of time. Now, begin with a relaxation technique. To do this just concentrate on your breathing, and slow it down…not so much that you find it hard to breathe, but a nice steady slow pace.
Astral Projection
Bring your focus to the centre of your forehead. Concentrate on this, but not too hard so that your head begins to ache.
Focus on the inner darkness of your mind, watch the blackness then push your mind outward. To do this, visualise a sort of white disc growing from your forehead and expanding outwards.
Now, begin to feel yourself start to float. To do this, sometimes it is good to visualise a spectral version of yourself floating free from your body. During this time you may experience some spinning.
If you feel confident that you do not need a spectral version of yourself, just concentrate on the feeling of floating.
Ending your travels
When you decide to finish, visualise your physical shell and float down towards it. Sometimes you will also feel like you are being pulled back, this is normal.
To completely finish contract your the white disc that you first created back into your head and open your eyes.