There should be three outputs from the small controller circuit board for step, direction and enable. These should connect to similarly labelled terminals on the driver module with a common 0/ground/earth connection. This assumes (always risky) that there is no need for pull up or down resistors on the three signal wires. If it works when connected fine, if not we can consider the fix to pull up or pull down the signals wires that needs to be done (it's simple but if you don't need to think about it why would you).
Connect the motor extensions to the driver module, this should be in accordance with the supplied information for the module. Connect the extensions to the motor tails.
Connect the power supply output to the driver module. If the input voltage for the board matches the power supply output voltage connect that up as well, if it is a different voltage you need a small voltage regulator board that can take the output from the power supply and reduce it to the voltage for the control circuit board. Connect the regulator to the power supply and then to the controller board.
Connect mains to the power supply and see if the driver module power lights come on, the motor will either lock in position or turn if there is any signal from the controller. The controller power light should come on. Pressing the controller buttons and turning the knob will hopefully get the motor turning.
So in summary, if the controller needs a different supply voltage than the power supply output a small regulator board is needed, otherwise you should have all you need to add some wires and try it out.
Martin C