Connect a wire from Arduino 5V pin to PUL+ and DIR+ on the drive. Connect a wire from PUL- to one end of a 330 Ohm resistor (1/4 or 1/2 Watt), connect other end of resistor to the Arduino pin you want to be "PUL" (I like 9), do the same with DIR- and pin ( 8 ). The pins will be "LOW true" (active when output pin is LOW).
In the schematic I attached to the original post, DIR- and PUL- need a GND connection. If they are connected they way you said, aren't they missing the GND connection?
The power supply of the DM2282 is connected and has a GND, but doesn't the Arduino need a separate GND connection as well?
At the moment no pin is connected to the GND pin so how does the LOW signal do that? Maybe you know the electronic explanation for this...? Are the 9 and 8 pins connected to GND somehow on the Arduino chip?
As far as I can see you just connect to PUL+ and DIR+ pins to the Arduino 5v pin and connect the PUL- to your Arduino step pin and DIR- to the Arduino direction pin.