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I’m not sure what you mean by how do they work so I’ll address it by explaining at least one common misconception. The puzzle is constructed with 6 stationary centers and then 20 pieces that have multiple stickers on each. These pieces are solid plastic meaning that the relationship of stickers doesn’t change. There will always be a red white blue corner with a particular order, there will always be a green white edge piece, etc. Once you understand that, watching the colors move around is less intimidating as you start thinking them as individual pieces to manipulate.
Now as for how people speed solve, it’s about pattern recognition and sequence memorization and muscle memory. The core concept is that you recognize that one or more pieces are in one place and they need to move to their solved locations. Then you recall the sequence of moves that executes that swap and rely on muscle memory to do it quickly and not process each individual move. Its “common knowledge” that Rubik’s cubes can be put into a random scrambled state and there will always be a sequence of under 20 moves that solves them. But I promise, no cuber uses this fact in any sense. There is an unfathomable number of scrambles and sequences you’d need to memorize which is impossible. Instead, cubers tend to memorize algorithm sets in the few hundreds and use them in series to solve layer by layer. In addition, you are granted inspection time at the beginning of a solve in competition. You can preplan your first several moves and execute them without thinking while trying to look ahead and find your next pieces
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