To create a blurred image:

-change your shuter speed so the shutter stays open longer

-you can pan the camera while the shutter is open

In a low light situation:

-raise the ISO level

-use flash

-use a tripod to reduce shakiness

-use a fast lens

When to use Aperature Priority

-When you want some control of the depth of field

When to use Shutter Priority

-When you want more control on photographing a moving subject