Text in after effects can have animators applied at the character, word or line level. The animators work kinda differently to normal animated properties in that the property that gets animated usually doesn't have keyframes, but is instead controlled by a selector which is comprised of a group of controls that determine what part of the text is to have the modification applied. Normally you animate the selector to add animation to the individual parts of the text.
Select your text layer and choose
Animation>Animate Text>Position from the top menu or from the
Add menu for the animator group in the Timeline panel. If you add some X offset to the position property that appears in the new animator group, and play with the selector beginning, end, and offset values you'll get a bit of an idea.
Now once you've fiddled with it for a bit, and probably got confused, head on over to the manual and give it a read.
As far as Motion Blur goes, if you turn on motion blur for the layer, and make sure it is on in your render settings you'll be golden. If you want to see it while you're working (at the price of much slower previews) turn on motion blur in the timeline window. How you do all that is also (surprise!) in the manual.