The driver GND is to GND on the breadboard
PWM on driver is to 5V(out) on driver
on the other side:
GND on driver to - post on 12V battery
V+ on driver to + post on the 12V battery
OUTA and OUTB are to the actuator
I don’t understand the purpose of the breadboard. Why are you connecting the controller ground to the ground of an unused breadboard? Also, you should not leave the dir pin floating (it does not have a default value and could cause the outputs to rapidly switch direction). I recommend you connect the DIR pin to ground. Other than that, your connections sound ok to me (it’s not very easy to see what’s going on in the pictures, but I didn’t see anything wrong).
Those connections sound find (I don’t know offhand which Arduino pins are PWM outputs). I suggest you make those connections before you connect power and write a simple sketch to control the voltages on the DIR and PWM pins. That way, you’ll be less likely to accidentally connect them to something that could destroy the board.