The led driver im thinking of using has the use of A low frequency PWM signal can be used to dim the LEDs
Do you know exact name of the LED driver and PWM frequency range?
So can the PWM outputs of the Ardunio be connected straight to the PWM pin on the led driver without the use of transistors and resistors?
If you use 500Hz or 1KHz PWM pin from Arduino, you may still need a mosfet to get full range of dimming. Otherwise you can adjust PWM frequency of Arduino.
Do all the grounds of both power supplys and the Ardunio need to be connected together?
Highly likely Yes. need to know the LED driver though.
You may find my post useful. It is about PWM frequency on power LED driver. http://arduino.cc/forum/index.php/topic,51887.msg390972.html#msg390972