How do people in the matrix use their powers? Like for instance when Neo stops all the bullets, or Agent Smith moves super fast, or when Neo flies, or when Morpheus jumps really high. How do these people use their powers? Do they have to actively think about what they want to do (i.e. if they imagine it, it happens), do they have to move their body a certain way, etc. Basically, I am asking how to people in the Matrix use their powers. I am not asking why they have powers, or how they work. I am asking what it is like for them to use their powers; how they trigger their powers. Is there any official source for this?
"Powers" seem to be invoked by believing that one can do something, and then just deciding to do it.
Morpheus: Do you believe that my being stronger or faster has anything to do with my muscles in this place? You think that’s air you’re breathing now?… Again.
Morpheus: What are you waiting for? You’re faster than this. Don’t think you are, know you are…. Come on. Stop trying to hit me and HIT me.
Morpheus: I’m trying to free your mind, Neo, but I can only show you the door, you’re the one that has to walk through it. Tank, load the jump program…. You have to let it all go, Neo, fear, doubt, and disbelief. Free your mind.
And later, when Neo starts coming into his power, and is moving faster than was believed possible:
Morpheus: He’s beginning to believe.
One might question why one can't simply believe six impossible things before breakfast and hit the win button, but the world does still have rules.
Morpheus: I’ve seen an agent punch through a concrete wall. Men have emptied entire clips at them and hit nothing but air. Yet their strength and their speed are still based in a world that is built on rules. Because of that, they will never be as strong or as fast as you can be.
Basically, to do something, you have to actually be able to do it within the rules of the code. Neo, due to his connection with the Source, gets to essentially reprogram the rules as he goes (although he does still seem to have some limitations preventing him from being able to push an "I win" button), has a slight edge, but it seems he is still limited by his mortal preconceptions as to what can happen.
As The Architect explained: Neo is The Anomaly - the personification of the imbalance in the equation, which is the option of the choice for all enslaved humans. This imbalance comes from the need to create perfect Matrix, which by definition cannot be perfect as it's used to host fallible human consciousnesses.
In other words: Neo is Humanity's champion (The Choice Personified) and his power is the ability to rewrite code in a way he sees fit (but as he's still human being, he is limited by his own imagination still) and that power comes - indirectly - from all humans in the Matrix. He uses that power by simply changing locally the rules of the Matrix to suit his needs. It may be also called "a godmode" or "cheat codes" on the fly.
In yet another words - Neo is something of a system process with access to the core of the system and all it's resources, which cannot be terminated - as in termination will cause crash, and consequently (yay! Channelling the Architect ;-) the death of all humans in the Matrix - and system's credentials to control that Neo process are no longer valid...
I believe that it is based off of code that already exists. The code of the one (the prime program) existed 5 times before Neo came along. The code also included a way for people to free their minds (Zion is part of the control scheme). So, they do not break any rules, since the breaking of the rules is enabled by the Matrix itself. As such, everyone who can potentially use the powers have the code/knowledge in their mind of how to use them. Also, one could simply download a program into their head in order to use their powers.