How can I tell what type of capacitor to use with an electric motor, if any?
Does this motor already have a capacitor built in ...


The car has 4 motors, one per wheel. If the motors do have capacitors added, each capacitor will be an easily visible part with two leads, connected to the two tabs of each motor, marked with the red circles below. So a visual inspection should suffice. 


(Image source: DX.com)

Most likely answer: No.


  If the motor does need a capacitor, what would be the formula(s) I need to study to find out how to match the right capacitor with the motor I'm using?


There isn't a simple formula to determine capacitor size in this context: 


My general suggestion for a motor this size operating at 6 Volts or so is to wire up the highest capacity non-polarized capacitor (e.g. a 1 uF film capacitor from DigiKey) that will fit in the space around each pair of motor contacts, and is rated for 12 Volts or higher. Non-polarized because the motor is likely to be driven both forwards and backwards, so polarity across the motor will switch around. 


A definitive computed value for a capacitor is not a simple matter of a formula:


The capacitance required would be determined by the load of the motor, how much noise the rest of your electronics can tolerate, the amount of radiated electromagnetic emission the operating environment can tolerate, the internal resistance of the power source (battery), resistance of connecting wires, the control mechanism used for the motor (PWM or not), the commutation frequency your motor will operate at, and I have probably missed a few other factors.