Did you not see fhe schematic with the "IN-1" signal name on the input resistor of the darlington transistor ?
Be sure to connect the GND to the arduino GND.
So I need to connect a 5v source to VDD and and each of my arduino pins will be connected to each "IN".
I set a pin to high and that activates the transistor to power the relay.
And I connect ground to my arduino.
Do I have it all correct? I just don't want to fry my arduino.
Yes . That's correct. If you truly don't want to fry your arduino you might want to consider learning electronics. It is a little hard to use an arduino without having to deal with it.
The important point with a relay is to keep the coil side of things separate from the
contacts - they are already isolated, don't lose that protection. Thus motor and ESC
stuff only to the contact terminals, Arduino control only to the relay driver connections.
[ Oh yes, the other thing, if you switch the relays while the ESCs are still powering
the motors, bad things will probably happen, so sequence stuff carefully. In particular
don't kill the Arduino / relay driver power while motors are running. The underlying
problem is that an ESC connected to a motor by two wires only (even for a very short
space of time) may conduct far too much current and burn something out. ]
Have you actually tried reversing two of the three wires between the ESC and motor to see if the motor runs in reverse? If so, two of the three wires could be switched with a relay like below. The 35ma relay coil current might be a little high for an arduino pin to directly supply.