yes gnd are smoothed and i use a 9v battery.
Wire-connection:
9V pin to Rainbowduino Vcc
GND pin to Rainbowduino GND
Arduino GND pin to Rainbowduino GND
Arduino RX (pin 0) to Rainbowduino TX
Arduino TX (pin 1) to Rainbowduino RX
Arduino RESET to Rainbowduino DTR