All grounds should be connected together. Can you post a full wiring diagram? Hand drawn is fine, please no fritzing, we hate fritzing here. Also, what makes you say it doesn't work? (ie, what are the symptoms?)
Sounds like a lack of decoupling on the power wiring. Alternatively it could be your power supply is not up to supplying enough current.
Could you explain the decoupling?
http://www.thebox.myzen.co.uk/Tutorial/De-coupling.htmlBasically you need at least a large electrolytic across the supply for driving stepping motors. Otherwise the ripple current can be too much for the driver board's ceramic capacitor.This is what can happen to the drivers:-
Maybe they are inadicuate?
That should be fine. If it were me I would also include a 0.1uF ceramic capacitor across those two big ones to cope with the higher frequency.The only thing I would change on your diagram is that you have the ground of the motor driver connected to the ground of the Arduino. There is also a common ground provided by the power supply being the same source so this wire is acting as a ground loop. I would try disconnecting this.So the circuit looks OK maybe it is your layout giving you problems, make sure the wires for the motor are not running along side the Arduino wires.