The blue ground wire on the left needs to be connected to the Arduino ground.
BTW, I think you could have the motor control you want without the SSR.
If you separated the yellow wires on the left and take them to two Arduino pins, turning one of the relays on will power the motor in one direction or the other depending on which relay is on, both off (or both on!) will turn the motor off. In this configuration, the gray wire from the relay outputs goes directly to the 12v ground. The ard on/off wire is replaced by the second yellow wire.
If you wired it without the SSR, your arduino code would look something like this:
void motorOn(boolean direction){
// turn one relay on and the other off
digitalWrite(pinM1, direction);
digitalWrite(pinM2, ! direction); // set pinM2 to the opposite of the value given in the direction argument
}