Interestingly, if an astronaut pushes himself away from the spaceship, the ship itself will accelerate in the opposite direction by a tiny amount (unlikely to even be noticeable to anyone in the spaceship). It will move far less than the astronaut because the action is controlled by the equation force = mass times acceleration. Force is the same for both, so the smaller mass will have greater acceleration.
Aeroplanes also change their vector by thrust as well as aerodynamic pressure. When you point the nose of an airplane in a different direction it means you are also pointing the thrust from the engines in a different direction. The engines will push the plane in whatever direction it is facing, and rockets on spaceships do the same thing.
Also, the F-22 Raptor is an example of an aeroplane which uses its thrust to change bearing. It can move its engine nozzles up or down in order to change the way its facing rather than just relying on aerodynamic pressure on the control surfaces. Another more obvious example of thrust vectoring on an aeroplane is the Hawker Harrier, which can manoeuvre at slow speeds by rotating its engine nozzles, without needing any assistance from its aerodynamic control surfaces at all, making it probably the best illustration of how a spaceship manoeuvres without looking at the spaceship itself. Alternatively, look at those odd fan boats that are popular in the Everglades. They rely on thrust vectoring alone to change direction.
