Your Arduino Uno, DRV8833 Motor Driver, Gearbox Kit will work together.
But I can't find example code of someone who has used it with the Arduino.
Not even in the forum of Pololu. So you have to find your own way how to do this.
Read the datasheet of the DVR8833, try to understand figure 1 and table 2.
Start for example only with fast decay, you can always add slow decay later on.
Pololu recommends to use the 'stall-detector'. This is a current limiter, which is disabled by default on the DRV8833 board.
But that's for later.
Connect one motor to the output A1 and A2 of the DRV8833 board. For example the '+' of the motor to A1 and '-' of motor to A2.
Connect the other motor to output B1 and B2. Use the same as for the other motor, so the '+' of the motor to B1 and the '-' of the motor to B2.
The inputs are inputs for the full H-bridge.http://en.wikipedia.org/wiki/H_bridge
Connect the input signals of the DRV8833 board to the Arduino.
Digital pin 0 and 1 are used for serial communication, so you could use 2,3,4,5 or other digital pins.
Also connect the ground and motor power, as shown in the picture at the Pololu page.
Set the pins of the Arduino to output: http://arduino.cc/en/Reference/pinMode
If a pin needs to be zero, use: http://arduino.cc/en/Reference/digitalWrite
If a pin needs to be a PWM signal, use: http://arduino.cc/en/Reference/analogWrite
If you are a beginner, you should use those functions first to blink a led (pin 13 of the Arduino Uno is a led), and to dim a led with the analogWrite function. So you know how to use them, and what thay do.