4 high torque motors (http://www.pololu.com/catalog/product/1591), and 2 motor controllers (http://www.pololu.com/catalog/product/1110).
Right, under motor specs it says that stall current is 2.2A, where Your chosen motor driver can only provide continuous current of 1A, meaning that if for any reason motor gets stalled for longer time, motor driver will most likely get fried. Also, when motor is starting to move or changes direction, current draw can be double rated stall current, meaning that peak current can be expected to be around 4.4A, where motor driver can only supply 3A.
I am just wondering how much power I would need to power it.
Worst case scenario is that all motors operate near-stall condition, so total curent draw then would be 4 x 2.2A = 8.8A @ 6V = 52.8W. If all 4 motors have to change direction at the same time it is possible that peak current draw can climb to double stall current in each motor, so 4 x 2 x 2.2A = 17.6A @ 6V = 105.6W. You should avoid these cases if possible. Normally You want to drive motors at no more than 75% their capabilities as well as use smooth acceleration and de-acceleration, this way it is more efficient.
Do I just need to power my microcontroller and it passes that energy through the motor controllers to the motors?
No, microcontroller is not capable of such high current output, motor drivers need to be plugged to power supply.
Also, if I want to stop one motor while leave the other on, could I do that with only 1 motor controller?
You should be able to control motors independently.
Finally, do I need to add the power consumption of all the parts to find the correct power amount?
That would give You worst case
, which should be avoided if possible. Normally you are aiming for average consumption to determine power source capacity required.
Try this calculator --> http://www.societyofrobots.com/energy_calculator.shtml