Hi...the three thin wires with the servo connecter should be connected to the arduino as if it was a servo. The white wire is the signal that connects to the Arduino output pin. The blck wire should be connected to ground. The center wire has +5 volts and should not be connected to the arduino (unless you want to use this to provide the +5 volts to power the arduino)
The three thick wires are connected to the motor. (you can reverse any two of these wires if the motor turns in the wrong direction). The two thick wires connect to the battery.
Use one of the Arduino servo libraries to drive the controller. Most need arming by sending a minimum throttle signal. Check the instructions that came with the controller to find out what pulse width this is.