[apalrd]

PID stands for Proportional-Integral-Derivative
Each is a "term" and the result of each is added to get the motor motion or change.
Proportional is, well, proportional to the difference between where you are and where you want to be. Basically, you say error = want - at, and then multiply that by a constant that testing reveals to be correct (the highest number without too much overshoot). Integral is the integration (sum) of the already corrected error, and gives the offset that should have been previously corrected.Derivative adjusts the rate of change by determining the slope of the error, the rate of change. This helps to even out noise.
Each term is multiplied by a gain that is statically set and manually tuned - this determines how much affect each term will have on the final output. It is also possible to switch from several gains based on set conditions, for example if you have a multi-jointed arm you might change the gain of the shoulder based on how far out the end-effector is from the shoulder, to prevent tippage when far out but allow it to move fast when tucked in.
PID is used in closed-loop control, basically you set a setpoint and it actively works to achieve it. This can implement itself in various ways, such as checking the angle of a potentiometer and adjusting it with a motor (used for angle control), checking the speed of a motor using an encoder and making it correct (useful for shooter wheels or such that must run at a certain speed), or even during autonomous to get the accumulated angle of a gyro and turn the chassis to acheve the desired angle, or setting the distance to travel and actively trying to get there without overshoot.
The standard FRC LabVIEW installation includes a PID toolkit - that can help. All you need to do is set the gain of each term.
If you want to learn how to do I would recommend implementing the simple Proportional control, tuning it, and seeing how it works. If you have problems, add either I or D depending on the problem. If you still have problems, add the other one.
One very very important thing to remember when working with potentiometers - if you turn them past their limit, they will break. Make sure that a positive motor direction = positive change in voltage. If this is not so, multiply the output by -1 or swap the wires on the OUTPUT side of the speed controller or the motor input. You could also swap the RED and BLACK wires on the pot.

As for where to start....
If you have large articulating structures on your robot, the most useful would be to use a potentiometer and a motor to control the angle. This would allow you to baically have a giant servo.
If you want to do autonomous stuff, then try to control the rotation (X on an arcade drive) using a gyro and a desired angle. When you get close to the desired angle, it will automatically slow down as the gain decreases and you will have a perfect turn.
And one last tip:
Always limit the output to -1 to 1. This is the range of the output and it is always good practice to do so. Do not rely on the WPIlib to do it for you.

And wikipedia has an article on the subject.