if the dog is moving, then yes a fast shutter speed will help stop any blur
if you want the background out of focus, but the dog in focus, select the largest aperture number you can and try to maximise the distance between the dog and the things in the background
for portraits, again you need a fast enough shutter to stop any movement blur (either from the model or the camera shake)
think of it as a triangle, shutter speed, aperture and iso (sensitivity to light), if you make one larger/faster then one of the other 2 will have to be adjusted too else your image will not be exposed correctly
eg ... fast shutter speed, large aperture number = low iso number (ideal for a portrait or dog moving, as fast shutter stops blur ... large aperture number makes background out of focus, and low iso = not a lot of digital noise (grain) on the picture
or ... small aperture to get everything in focus (dog and landscape), fast shutter speed = high iso (lots of noise)
of course all of this depends on how much light is availiable from that big yellow thing we see every once in a while in the sky ... and how many of those big fluffly light diffusers are infront of it lol
hope thats of some help
Phil