I keep thinking on how to respond to this, and supernaturalists will differ on this but I kind of see it as mostly psychological and spiritual... it's kind of like a meta-art... but it's more than that.
I used to believe in supernaturalism so maybe back then I had a more straight forward answer. I just know I still use the same mechanisms, I just interpret the experience naturalistically as an expression of our minds and subjective realities.
It shapes and reshapes you, mentally and spiritually. It can be a great tool but also a great pitfall. Tinkering with the mind like that can be hazardous if you go in deep into certain things without knowing what you are doing (mostly black magic). I personally use magic in my own path to help me spiritually. Sometimes I am trying to get rid of something negative in my life (thoughts or habits) or maybe I just want to use some kind of emotion or desire and transmute it to help me transform part of myself.
I guess really for me I stopped seeing magic as something to manipulate the objective, physical world but still use it to manipulate the subjective, spiritual-mental world. This can work on other people too but I wouldn't do it in most cases unless the person asked. I can't really think of a lot of good examples to ever use magic on someone without their consent as that is basically abuse of sorts.
To me.. magic and the mystical experience are the same... in some forms of yoga they call them siddhis but to others they call them magical powers. In either case it's all the same to me and really both can be distractions.
To use it I normally utilize meditation and/or rituals... symbolic gestures and the like. Mantras too can do it for me if I am in the right state of mind and keep reciting a mantra. I've had forms of Devi speak to me most often as well as many lesser spirits. A few times Shiva showed me something, almost always when meditating though. It seems Devi only really comes to me through mantra or when outside on a new moon.
As well I find using yantras and mantras together can help me (at least percieve of) moving around energy as to how certain yantras seem to indicate certain truths... sometimes I can do this to realize another meaning of a compodent of a yantra or other symbol to help me learn a spiritual or personal truth.
I guess other people do stuff like presented in witchcraft books or neo-paganism, new religious movements ect. Lots of stuff with phrases, symbols and steps you take ect but then sometimes just what is commonly called "energy work" which seems very popular these days. I know a lot of people in real life who are practicing Reiki for example and I'd consider that magic, energy work to be specific (though I'd caution anyone to never use it as a replacement to real medicine). I could get more specific but the approach is really diverse and I'll leave it up to others to describe what their path does
Anyways that's the best answer I can give at the moment... I might have a better one later. Like I said, I think it's basically the same underlying mechanism in all religions, we just tend to have different takes on it. Even abrahamic prayer is, as relatively weak as it generally is, is still a form of magic in my opinion. Though if done with enough conviction/belief it can be just as powerful as something much more magic-y.