Motion blur and blurred background?

How do you capture motion blur and blurred background images in manual mode using a Nikon? I would also like to do close up shots like that too. What are the potentials of this type of shooting? Would I be able to do a close up of say an eye lash, while blurring out the rest? Ridiculous example but I would like to know the limitations

Motion blur is more where the camera is moving with the active object, that the captured image gets still of object, but everything else is in motion of the sequence.

http://www.digital-photo-secrets.com/tip/4189/mastering-panning-photographing-moving-subjects/

The blurred background and / or foreground is termed, where lens settings are focused in range of the captured object only, so focal point is specific to object, and everything else is diffused or termed aberration skewed.

http://www.slrlounge.com/school/aperture-guide-pt2-shallow-and-deep-depth-of-field/

This is different motion blur as more to do with time lapse sequence to set shutter open longer, but lower exposure.

https://ww2.lifepics.com/Photography-Tips/using-manual-mode.htm
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Capturing motion blur is done through a few techniques either alone or together. First, you need a shutter speed slow enough to blur just the parts you want to be blurred. At 1/1000th a sprinter is going to be stopped, but at 1/125th the feet and arms will be blurred. However, you need to know how to pan with the subject using this long of a shutter speed. Panning is basically keeping the subject steady within the confines of the frame so that relative to the sensor, the subject is not moving. However, as you move with the subject, relative to the sensor the background is now moving very quickly. So with the combination of a good panning technique and a slow-er shutter speed, you not only get the motion blur of the subject (to some degree) and blur the background which just magnifies the feeling of speed.

To blur the area behind the subject, you need to use a shallow depth of field (dof). DOF is defined as the area that appears to be in focus in a photo. It's controlled by three things:'
1. Focal length - The longer the focal length, the shallower the DOF. This is important to consider when buying a camera because the larger the sensor, the longer the focal length will be for any given angle of view. This is why it's nearly impossible to blur out backgrounds with a camera with a 1/2.3" sensor, but not an issue with APS-C or 35mm format sensors. With a 1/2.3" sensor 15mm lens has the same angle of view as a 50mm on an APS-C or an 80mm on a full-frame camera.

2. Focusing distance - The closer you get, the shallower your DOF. Therefore, your eyelash example would easily have a very shallow DOF, even on a 1/2.3" format camera.

3. Aperture - The aperture is the most common way of controlling the DOF. The smaller the lens opening (larger f/stop numbers), the greater the DOF. So using a lens with a maximum aperture of f/2.8 or larger such as f/1.4 will produce a very shallow DOF, while the same lens shot at f/22 will have a much greater amount of DOF.

So, depending upon what format of camera you're using, and what lens, you can easily get the eyelash in focus while the pupil will be out of focus. This, of course, depends if you're focusing close enough.

To get motion blur, shoot in shutter priority or manual mode so you can select the shutter speed.

Choose an appropriate speed for the motion you want to blur.

For out of focus background (it's called shallow depth of field), you need;
- a wide aperture (ie small f number, like f2.8)
- a longer focal length (ie 50mm and up)
- a close camera to subject distance vs a much larger subject to background distance

In the particular example you mentioned, you would almost certainly need a macro lens - this allows the very short distances between subject and camera and inherently has a shallow depth of field.