There are a few ways to do this. As there are some things that can be done in photoshop. There are a few things that are done with in camera which will make movent look good.
One of them is playing with camera settings to a slower speed so as what you are shooting is going by and the back ground is moving. This way normal looks the best as it is in the camera and not afterwards.
Then you have photoshop, where you can cut out the parts you went to keep still then you can use motion blur the back ground. Which gives it a differnet look then to shooting it in camera as normal you have to remove the subject off the background, before bluring it.
There is a big difference between shooting in camera and photoshop. Personal, I like anything I do done in camera as that is how it should be. As in the old days it is a lot more difficult to do this after shooting.
I hope this helps I will go thought more like this.