The Fritzing diagram for the robot is shown below. The number of parts and connections is fairly low. Hookup wire for the breadboard makes for sturdier connections than premade breadboard wires.
The alligator clip to male jumpers allow connection between the Circuit Playground and the robot. You can buy them from Adafruit as part #3255 or make them yourself from clips and pins.
Peel the adhesive off the mini breadboard (or put some adhesive on the back if the breadboard lacks it) and stick to one side of the robot body defined by the two servos. This will be our wiring side.
We need to attach the servo leads to the board as shown. Cut individual 90 degree header pins and take off the plastic square. Make 6 of them. Place them on the locations in the 4th row from the top with the ends pointing to the "top" defined as where the servo wires are at. This allows for good breadboard and servo cable connections. Add red and black solid wire to be able to power the servos off the same battery voltage.
Next add the alligator clips, connecting the two white servo control wires and the two joined power lines. I suggest Black for ground GND, red for power VBATT, and two other colors for the servo control wires. In the picture below, I did not have the newly stocked Adafruit multicolor cables.
Take the LiPo battery and stick it to the non-breadboard side of the robot body with the power lead sticking out towards the left wheel. Use Blu Tack, thick double-sided tape or other non-permanent adhesive. Place additional non-permanent adhesive on the back of the Circuit Playground board and carefully press it onto the battery at a 45 degree angle.
The Circuit Playground should be up a bit so that when we drape the alligator clips over from the breadboard side, they comfortably clip onto the 4 top pins (one reason we tilted the board at 45 degrees, the other two being good for the power and USB connectors).
The joint red connections on the breadboard go to the Circuit Playground VBATT connection. The joint black connections use the clip that is connected to the Circuit Playground GND connection. The right motor (looking from the breadboard side) goes to Pin #6 and the left motor connection to Circuit Playground Pin #12.
That's it. Check your connections against the diagram and pictures to be sure everything matches up.