Philthy:
Okay. So, it is really dependent on the voltage of the motors being used. If I have two 3V motors, I would want around 3V (or higher) of whatever battery type I want. If I choose 6V motors, I would want around 6V (or higher) of battery type, 12V motors around 12V (or higher), etc etc?
It depends.
Some motors rated at one voltage can be run at a higher voltage, although life of the motor may be shortened (bearing and commutator, mainly). Some can be run at a lower voltage than their rating; depending on what kind of "cogging" effect on the rotor there is, you can sometimes run a motor on a fraction of its voltage rating (note, though that torque will be affected). For instance, I have a 90 VDC motor that I can run fine on 12 volts (and it still has quite a bit of torque - it was a motor for a treadmill).
Generally, you don't want to push a motor beyond 10-25% of its voltage rating; for the longest life, though, don't run a motor at a higher voltage than it is rated for.
Philthy:
So long as the motor controller allows the selected voltage to be run off of it.
Correct.
Philthy:
That 293D chip says 4.5v-36v, so I would NOT want to use 3V motors with it reliably correct?
Well - there is always going to be an internal voltage loss on the h-bridge; you might find that you could supply it 4.5 volts, but the output hovering around 3 volts, in which case you -could- use it with a 3 volt motor. Read the datasheet; it should have some info on this.
Philthy:
Also, if I went with 4 motors (dual 293D board), nothing would change, the battery would just get drained quicker? That is where the mAh comes in to play when choosing.
Depending on the mAh rating of the battery, and the mA ratings of the motors.
I'll try to explain more in a bit...
Philthy:
That 3.7v battery would be good for 3V motors and a controller that also supported that low of voltage, yeah?
Yeah; likely with motors that small and a small battery, you would use a discrete transistor/mosfet h-bridge (and depending on your needs, those transistors/mosfets might all be SMT components).
Philthy:
(Hope I am getting this)
I think you're on your way... 
Philthy:
So then, if all that above is correct. Where does amperage come into play? I am guessing this is why a 9V square battery wont run jack, because it can't pump out enough juice at once? I don't see amps listed by batteries, so this looks like another stumbling block.
Most batteries (or cells) don't have that information listed on them (many rechargebles do, though); you generally have to look up the datasheets for the batteries at the manufacturer's website - so when in doubt, check there. You can also get a good idea what certain cells/batteries can supply (on average) from wikipedia (can't find the article right now, but there is one out there - somewhere).
Now - to explain amp-hour ratings and how long something will run...
Let's say you have a motor that draws 1000 mA (1 Amp), and you have a battery that has a rating of 1000 mAh (1 Amp-Hour) of capacity. That means that motor can run for one hour (this isn't completely true - but accept this as "true" for now). If the motor was rated for 500 mA (.5 Amp) - then it could run for two hours off that same battery. Now - what if the motor drawed 2000 mA (2 Amps) when running? Could you still use the battery?
Sure you can! How long would the battery supply current? It would supply the current for .5 hours (half-hour). See how the math works? Simple division/multiplication.
Now - as noted - this is called an "ideal" situation. The truth is worse. You won't get these numbers and times, even if both are rated the same way. This is where the datasheet of the battery comes into play.
You see, when you draw current from a battery with a load, the battery heats up (caused by the amount of current being drawed and its internal resistance - the resistance is noted on the datasheet, btw); this changes things drastically. The change is called a "de-rating". Other things can cause further de-rating of a battery's capacity (mainly external temperature; humidity can also come into play - but the main factor is temperature). On the datasheet, they note all of this - you'll find a "de-rating" curve graph (or maybe more than one) that will show you how these factors work against you.
So - in reality - you'll never get 1 hour of run-time with a 1 amp motor on a 1 Amp-Hour battery; more than likely, it will be around only 30-40 minutes of run-time, and that at only a certain temperature (some kind of ambient room temperature - 70 degrees F, for instance); with higher or lower temperatures (both external, and internal to the battery as it is used) this will change. If you want to know your "real" run time, you'll have to take that into account as well.
Hope this helps to explain things...
