I currently have a DC motor (G&G 18000 RPM Long Motor for Airsoft AEG ) connected to a MOSFET with two sensor cables. I will be attaching the MOSFET to an external battery, but was wondering how I would be able to connect the two signal wires to the Arduino and the code that is needed to complete the circuit. I am very new to this, and have no experience with working with DC motors on an Arduino. For reference, here is what that looks like right now http://imgur.com/a/eMzKs
Unfortunately, you have provided little information on which to provide a response of any meaning. You really need to include the part number of the mosfet, the voltage and current requirements of the motor, and exactly what type of operation you need it to perform. Are you looking to press a button and have the motor spin? Does the motor spin when the lights come on? We can only guess. You actually know.
Is that a logic level mosfet? If not then you need to get a logic level mosfet first.