I think the key (and I'm saying this as a fulltime programmer), is to learn how to see things as an artist. I had a fantastic art teacher my last year of high school, and for a month or two, I think I understood how to look at things in a different way. I have two drawings and a painting from those few months, and they're some of my favorite possessions.

I've since forgotten how I managed do make them, but I think that's largely from a lack of practice.

I feel a similar way when trying to learn something new that looks/feels like magic. The tutorials are simple enough and give awesome results but for some reason I don't get it. After much practice eventually something clicks and it turns out that there was no magic, it really is as simple as claimed.

I think that it seems like magic to us because our brain refuses to believe that it is that simple. But specially because we lack the practice. After much practice eventually a threshold is reached and the brain decides that you've been exposed to enough patterns and nothing else is left to learn and that is when "it just clicked" happens. At least that is what I think is happening. Your brain is protecting you from claiming you've learned something new without enough practice.