I also added two LEDs to the project, just to visualise the effect of REST calls. But you can also add analog or digital sensors to the project to test other functions of the library.
To connect the breakout board, connect the IRQ pin of the CC3000 board to pin number 3 of the Arduino board, VBAT to pin 5, and CS to pin 10. Then, you need to connect the SPI pins to the Arduino board: MOSI, MISO, and CLK go to pins 11,12, and 13, respectively. Finally, take care of the power supply: Vin goes to the Arduino 5V, and GND to GND.
For the LEDs, I simply connected each of them in series with a 220 Ohm resistor, on pin number 7 and 8 of the Arduino board. The following picture summarises all the hardware connections: