Once the spacecraft is armed with knowledge of where it is pointed and how fast it is turning, the question becomes how to change these things. That's where the control devices come in.
These thrusters change the speed of the spacecraft's rotational (spinning) motion. They are unlike the other larger thrusters, which are used to change the linear velocity of the spacecraft -- that is, its speed along a line. The reaction control system thrusters are good at making quick turns, and are used for getting to new orientations quickly. They also work with the reaction wheels in a special operation described below.
The reaction control thrusters are arranged in "couples" -- pairs of thrusters that together can spin the spacecraft without giving it any lateral velocity. If one of the thrusters in any of these couples fails, the other one can do the job almost as well, but the single thruster will add some lateral velocity. That's okay as long as navigators can measure it and take this change into account in their subsequent calculations.
While the reaction control system thrusters allow the spacecraft to turn quickly, they're not good at slow and steady turns. Slow and steady turns are required to take high-resolution images of Mars from orbit. Mars Reconnaissance Orbiter therefore has devices called reaction wheels. These are literally spinning wheels -- four in total: one for each rotational axis plus a spare in case one of the three isn't working.
These wheels can be spun at variable speeds using electric motors. If the spacecraft needs to turn in one direction, it changes the speed of one of the wheels in the opposite direction. In effect, it pushes the wheel faster or slower and, as a result, the spacecraft gets pulled in the opposite direction. If you've ever ridden the Magic Teacup ride at Disneyland, then you get the idea! Each wheel weighs 10 kg (22 pounds), and can be spun as fast as 6,000 rpm (revolutions per minute).
Now, you can't spin the wheels faster forever. At some point you must slow them down and start over. Of course, slowing the wheel will make the spacecraft turn in the opposite direction, and you don't want that once the spacecraft is pointed in the right direction. That's where the reaction control system thrusters come back in: they are fired to push against the force resulting from slowing down the wheels, a procedure called "angular momentum desaturation." The two opposing forces essentially cancel each other so that the spacecraft remains in the intended orientation.