/u/Eulers_ID did a far better job explaining the mechanical ways rocket ships maneuver than I could ever hope to.
The really general answer is that rocket ships work on Newton’s Third Law: Every action has an equal and opposite reaction. This means if you’re in space, and you throw a bowling ball away from you, your arms are also “pushing off” of the bowling ball, so you’ll be recoiled backward.
So, to maneuver in space, a rocket ship just needs to “throw” something (fuel exhaust, ions, or heck, even bowling balls) in the opposite direction that it wants to move. The change in velocity (rocket scientists call this “delta-V”) is the mass of the thing you’re throwing, multiplied by how fast you throw it away, divided by the mass of the rocket. (Not exactly brain surgery, eh? :D)
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