Motion blur is a brilliant way to broaden your photography skills, putting movement into a shot can add an extra element or depth to the shot, it takes practice but it is definitely worth it.
There are different ways to capture motion but all require you to slow your shutter speed, obviously it depends what you are shooting and the effect you want to achieve as to how much. As you already know the longer the shutter is open the more exposure you will have, so make sure you turn down the ISO and use a smaller aperture.
Panning is a technique where you move with your subject to create a blurred background, it can be very difficult to master but the results can be very good. You regularly see these shots with motor sports as they are a great way to convey speed.
Another way to use motion blur is by setting you subject in a stationary position where you know the background will be moving, roads at night are a great example of this where the road and surrounding area are still but the lights from vehicles leave trails across the shot.
Alternatively you can create a varied type of picture by shooting a subject and moving the camera simultaneously. When taking these types of shots try to follow existing lines for example if you move the camera in an upward motion and follow the natural line of a group of trees (as pictured) you can create an completely different type of shot.
As with everything new try it out and practice what you like, it will help you develop your repertoire and style.
Mclaren image by Bernard Chang III