Start off by creating a new file, and making a background in whatever style you like.

Use the text tool to create a new text layer, type whatever saying you would like to animate

Lets make it look a little better by adding a dropshadow. Duplicate you text layer, and change the color of the lower of the two to something darker than the text above it. Move this layer one pixel to the right and one pixel downward.

Rasterize both the text layers by right clicking on the layers in the layer window, and choosing "Rasterize Layer." Merge them together by pressing Ctrl+E while on the top layer.

Now we are going to duplicate this layer 3 times. While on your merged text layer, choose Layer > Duplicate Layer. Do this twice.

You should have something like this in your layer window.

Click on the middle of the three text layers, and choose Filter > Blur > Motion Blur. Use the settings shown below.

Bring up the animation window by choosing Window > Animation

Hide the top two text layers so your image look something like mine.

Create a new frame by clicking on the arrow on the right side of your animation window, and choosing "New Frame."

On this frame, hide your bottom and top text layers, and leave the blurred visible.

Create a third frame and hide the bottom two text layers, and a forth frame showing only the blurred text again. In your animation window, change the duration of your first and third frame to 2 seconds.

You test out your animation! You should have something like mine. The next step would be to change the text after it blurrs, so the sayings alternate, have fun with your blur text.