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From what I understand, a rocket changes its direction during launch by gimbaling its engines (i.e. swiveling the engine nozzles so the thrust of the engine points in the correct direction).
But what controls the gimbaling of the engines? Do engineers simply pre-program the sequence of gimbaling changes? Does the electronic logic on the rocket adjust the thrust direction based on altitude readings, etc? Or is ground control responsible for this?
First of all, it's worth to mention that engine gimbaling is not the only way to control a rocket. You can use differential thrust, or vernier thrusters, or even aerodynamic flight control surfaces. But you are right on that, that all of these systems require some sort of control.
The gimbaling angles can't be pre-programed, because they have to dynamically adapt to minute changes in the vehicle's attitude. (That is the word used to describe where the nose is pointing.) If, during ascent, a sudden gust of wind tips the rocket to the left, it has to counter-act with something which creates a rotating moment in the other direction.
Therefore the rocket guidance system works in a loop. It senses the current attitude. Compares that to a target value. Actuates in such a way that the error decreases. Then repeats. This is called closed-loop control. (As opposed to the open-loop control, what would be what you described, with the pre-programed gimbal angles.)
If you are interested in this topic, there is quite a bit detail about the Saturn V Instrument Unit on wikipedia. That's the part of the Saturn V rocket which among other things, provided the guidance signals to the engines. http://en.wikipedia.org/wiki/Saturn_V_Instrument_Unit
Rockets generally use an inertial navigation system (INS). This system uses the input from accelerometers and gyroscopes to calculate the rocket's position (relative to the launch pad) and attitude. This is a form of dead reckoning ("I have traveled x km at n degrees, so my position must be y").
The INS takes care of both navigation and error correction (compensating for e.g. wind gusts that change the rocket's attitude). INS can be used autonomously, but if you do that, tiny measurement errors build up over time so your end position is not entirely accurate. So there's generally an error correction mechanism: a system that can provide outside confirmation of the rocket's position. This can be a star tracker or a ground station that tracks the launch via radar.
The INS controls the steering system of the rocket (be it a gimbaling system, vernier thrusters or other methods).
In modern INS, the gyroscope is often in the form of a ring laser gyro, instead of the traditional mechanical gimbaled rotor.
In addition to the INS, rockets contain a sequencer, this controls aspects of the launch that are time-sensitive. The sequencer decides when to stop the engines of the first stage, jettison the stage and fire the engines of the second stage, for example.
