Additional power supply input for projects

I'm newbie, I have a questions. How can I connect a seperate power supply to arduino for modules like motors, particularly controlling motor speed?

In general, use separate supplies for Arduino and motors. Only join the grounds. Leo..

For motors in particular, where you often need to change direction as well as manage speed, you would typically look at a module like this. (They come in different voltage and current versions, and from different makers. I just put that forward as an example.)

As you'll see from the wiring diagram on that linked page, you attach the motor power supply to that chip. The chip passes that power on to the motor, but under the control of the micro-controller which takes care of direction and speed. As Wawa said, the grounds need to be hooked up, and you can see in the diagram that is the case.