How do gyroscopes work? Well, they have a number of properties, and they work primarily because an object in motion tends to remain in motion, until acted upon by an outside force.
Go out into interstellar space. Let me know when you get there.
Ok, so just imagine you have a disk of very strong steel, and five or six very powerful rocket motors on the edge of the disk, all pointed in the same orientation with respect to the periphery of the disk. (All clockwise, for example) We fire off all the rockets, and the disk begins to rotate. This being deep in interstellar space, there is almost no chance that the disk will encounter any friction, and the exhaust of the rockets has a pretty good vector away from the disk as well. So, we get no friction.
Now we have a gyroscope. Force has accelerated the disk, and the material (steel) allows the tensile strength to act as a centripetal force to make our linear acceleration become angular momentum. Now that the gyroscope is spinning, it has certain properties. One of those properties is that the axis of rotation (through the center of the disk, at a right angle to its surface) is more stable in it’s orientation with respect to the rest of the universe than a disk that is not spinning. If a passing molecule of hydrogen hits our disk off center it will have less effect on the orientation of the axis than it would on a non rotating disk, although it would move the disk the same amount through space.
The cause of this is the momentum of the steel in its circular path. To flip a non-rotating disk, you require only the energy necessary to move the mass of the disk. With a rotating disk, the energy of motion is already moving the disk, and to change that motion, you must have enough energy to effect all the current momentum, and then impart a new motion. This resistance to twist in the axis is experienced as “precession” of the axis. What happens is that your new force combines with the energy released by the momentum of the disk, and the resultant vector is at an angle to the force you applied. Any movement which the disk makes that does not alter the orientation of the axis of rotation is unaffected by the angular momentum. A lot of science fiction is based on the impression that gyroscopes have some hold on their position in space, and if that hold could be modified, we could move along magically without any thrust. Sounds so cool, but it just is not so. You can move a gyroscope as easily as any other object; you just can’t turn it around corners as easily.
Before someone brings up the disk rotating faster than light speed let me explain something. First of all, the tensile strength of such a disk is a number of orders of magnitude greater than the forces that bind atoms together. The disk simply flies apart. Secondly, the energy required to accelerate a disk depends on its mass, which would increase as its edges approached light speed. To have even the smallest part of the edges of the disk exceed C would require an infinite power source.