It can range from mental visions to dreams, to dream-like encounters during trance. What you see really depends on the energy you are interacting with, as the astral planes are vast. The etheric plane, which is tied to the physical plane (if you acknowledge its existence in your path), is a bit easier to "expect" as you have an environment you are already semi-familiar with. However, etheric projection tends to be more difficult if you've never tried it before. To start out, it might be a good idea to develop your psychic senses of the physical plane and then work on reaching out. You don't have to "disconnect" from your physical body to project, as some believe that projection is merely a shift in consciousness (if you believe in Subtle Body Theory in that we all exist in all planes at once).
What trips a lot of people up is the question you're asking - how does one experience projection if they have never projected? It's a catch 22 situation and honestly, it is easier if you drop your expectations and experience things as you go along (which a lot of people will tell you is easier if you are in an altered state of consciousness as our waking consciousness isn't as "connected" with outside reality as our subconscious is - when you're in an altered state, it's akin to bridging the gap between the conscious and subconscious minds).
When I was first introduced to astral projection, I was told to simply envision myself walking out of my physical body and aim for a different physical place. This tripped me up for years becuase what I was "taught" was etheric projection and not astral projection, making me think that astral projection was harder than it really was. It didn't help me at all because I had expectations and I didn't think I was meeting the predetermined expectations set for myself.
What we experience will be different from others, so instead of focusing on methods to achieve a state you don't know, simply let things flow. You don't even have to lose waking consciousness or be "separated" to be aware of subtle planes of existence. For some, and maybe for you, it may just be better to realize such connections and reach out through them. Don't be frustrated if you don't succeed right away, because this is entirely new territory for you. It'll take time to adjust, just like it takes time to learn how to ride a bike.