The energies that are involved in magic are not part of the spectrum of light, and so are typically not visible.
However, as you become more acquainted to them you will begin to be able to sense them more thoroughly. As the mind processes the sensation of these energies it can sometimes form images either within the mind, or as something akin to a visual hallucination, that allow you to "see" magic.
It is important in this to realize that any such image is your mind's way of interpreting the nature of the energies. Often a visual image is not the literal nature of the subject, but your mind's way of trying to tell you more about the subject.
If something is passionate, and full of energy it may appear almost akin to a flame, or with red tones, for example. This does not mean it is literally a fire.
Hope this makes sense.