You're confusing the blur in the background that's due to having a shallow depth of field with motion blur from a long exposure. The exposure length has pretty much nothing to do with it here.
It's all about the aperture. (And if you want to change your composition, the distance to the subject.)
Depth of field has been covered in great length on the site otherwise, so there's no need to repeat it all - but basically you'll want to get as close to your subject as possible, with the widest aperture (lowest f number) to maximize your subject isolation. Moving back or making your aperture smaller (bigger f number) will make the background more in focus.
If you only have a point and shoot camera with a small sensor, you'll be unlikely to replicate the subject isolation in these photos.
(Also, given the donut shaped bokeh of the first, its possible it was done with a mirror telephoto lens, which have relatively close focus for their focal length, giving them the ability to do some shots like this)