Let me clarify that I am not powering the motor WITH the Arduino board, I just want it to complete the circuit. The motor has its own power source. If I would not use the relay to do it, what would I use instead? I want it to be like a normal switch, like a light switch, but I need it to be able to turn on and off with the Arduino board.
It may have its own power source but the relay needs to be suitable for the power being switched.
If it is a small DC motor, no problems.
If it is a large 240VAC motor rated at 2kW, it may be a little light for the job. Unless the relay board is to operate a contactor that carries the motor current.
As you have not given any information about the motor or how it is switched we can only guess what your intentions are.
A relay is a switch, it only is activated electrically, not mechanically. The relay contacts are isolated from the activating coil, which is powerd by a digital output of your Arduino (eventually assisted by an transistor for higher coil voltage or current). Relays are available for various loads (AC/DC voltage and current), and for various activation voltages and currents. When you buy a relay shield for your Arduino, make sure that its contacts support the motor voltage and current. Then connect the contacts like you would connect an mechanical switch to your motor.
Another solution are "solid state" relays, which typically have an integrated opto coupler for isolation from the load, and an triac to turn the load on and off (AC only), or an power transistor for switching DC. Again check that the output supports your motor voltage and current.
Engine means it runs on fuel like gas of some kind.. If that's what the OP is using a small relay would work in place of the key switch But the relay would need to open once started from the motor starter and one stay closed on the coil side or fuel side. witch is the run contact on a key switch.
You start a engine three things happen the switch moves to run then to start then it falls back to run.
You no the engine started so you let go of the key you'll need to let the arduino no it started thats the hard part. Or should I say harder part.