I'm trying to learn about a very basic motor, the servo motor. Can these be found a thrift stores like Goodwill in old toys? Are these "robotic" quality? What toys or other kinds of things would I scavenge? All I want to do is get a motor. After that I want an Arduino and make it "work." Nothing complex.
While some people scavenge even for cheap parts, I do not do that, simply because it will cost you more than just ordering the exact thing you need and knowing it is working. Don't forget that you probably have some specific requirements, i.e. the servo must be of some size, have some torque and so on...
Majority of toys (if not all of them) you will find at Goodwill will have just a basic DC motor with minimal feedback and won't probably as a 3-pin plug&play servo. These are not even required to be the same in identical toys, simply because manufacturer will use the one that is cheaper. This means the properties of the motors may be different and to tune your control loop to get two motors running at the same speed will cost you the same as just buying a working part with known characteristics.
EDIT: Since it seems like you are contradicting yourself in the question I would like to make it clear that a servo motor is not the easiest to use, since besides power it also needs a signal that determines where it will turn. A typical servo motor you will find looks something like this.
On the other hand, the easiest motor to use is just a plain DC motor. They look something like this, although there are many models of them that may even look different. To turn this motor you just need to supply power to it. The polarity of the wires determines the direction in which it will turn and the voltage determines the speed.
A servo is not a basic motor - it's a motor plus some means to control its position. If you want DC motors. A small servo costs around £1.75/$2 new for 1-10 quantities. Servos have three wires going to them - ground, power, and a pulse width modulation signal to control them, which is fairly easy to generate with a microcontroller.
Plain DC motors are electrically simpler - you provide power as DC and they move one way or another depending on polarity - but require more driving electronics as a microcontroller cannot provide enough current. So you would need either an H-bridge to drive it both ways, or a power transistor to drive it one direction only. A small low-quality DC motor costs about a pound, a higher quality motor (such as you'd get in a model railway locomotive) ten or a few tens of pounds. An H-bridge to drive it, such as L298 costs a couple of pounds, so if you want bidirectional drive it's probably worth buying a better motor.
The prices above are for hobby kit; industrial robotics motors are typically ten times more expensive, so if you mean industrial by 'robotic quality' then it's unlikely you'll find something in a second hand store.
Buying scrap equipment and salvaging the motors from goodwill is unlikely to give you better quality or consistency than buying cheap motors new. You may get lucky and be able to buy a toy with a few hobby quality servos in it for less than $$2 per servo, or you may have a project in mind which needs a higher power motor and so buy something like a sewing machine for less than the cost of an equivalent motor (~$20), but unless you're lucky it's probably not worth the candle.
So be lucky!
Not servos explicitly, but I've obtained low end nema 17 stepper motors on occasion from electronic typewriters at goodwill. The typewriters I've seen there usually have 1 such motor in them (in addition to some other neat pin mount components) and fetch for $1 each. In my case the only other source for parts is radio shack and online outlets, so for me it's a viable option if I don't want sit around waiting for orders. This is however not a reliable method at all, especially if you want parts in large numbers or with certain specifications.