Non Blur Nikon Settings?

What would be the best settings for a D3100 Nikon with a AF-S nikkor 55-200 mm 1:4-5.6G ED lens, for the best clear, sharp, non blur images without a tripod or monopod.

Set camera to A mode, lowest f/number and ISO 1600. If you are shooting in low light without movement, that would be the best you can do. If there's no blur and you find the picture too grainy, lower ISO. If there's blur, raise ISO a bit and expect more grain.

Under what lighting conditions?
If bright sunshine, then let the camera do the thinking for you. Set to Auto or Av or TV and go by what the light meter in the camera tells you.
If low light then increase the ISO, and combine selecting wider aperture and/or selecting slower speed.
There's not a single universal settings we can recommend; every situation is different and needs thinking about.

You need to learn how to balance ISO, shutter speed and lens aperture.

If your shutter speed is set to 1/500th second, almost all your images will be sharp and not show any blur.

What that means is that you need to use your lens wide open and adjust the ISO up as high as it needs to go to assure a shutter speed of 1/500th second

See the link below

Sounds like you are talking "Depth of Field". Using the smaller lens openings or aperture settings will give you the most depth of field. I usually use the "AV" setting and set my camera the highest f/stop and let the camera choose the shutter speed. Shutter speed? YOU need to know what shutter speed you can hand hold the camera at. When I was a teenager, I could hand hold as low as 1/30th of a second. Today with age comes 1/200th. If I were you I would buy volume "one" of Scot Kelby's books.

The Digital Photography Book: Part 1 (2nd Edition, by Scot Kelby

Available on Amazon for about $15.00

In order to avoid blurred images due to camera shake on a handheld camera, you generally need to set a shutter speed equivalent or greater to the reciprocal of the lens focal length.

So on your 55-200mm lens, you'd be looking at shutter speeds ranging from 1/55th of a second to 1/200th. Usually you can't set those speeds exactly in manual or shutter priority modes, so need to go to the next highest speeds of 1/60th to 1/250th. If you use any lens with vibration reduction built in then you can usually get away with shutter speeds up to two stops faster, so using the example of your lens and pretending it has shake reduction, you'd potentially be able to use shutter speeds of 1/15th to 1/60th. In practice, for various technical reasons regarding how many axes of shake reduction are controlled, you'd realistically get away with just one stop faster, so 1/30th to 1/125th.

Those are just the shutter speeds; depending upon the available light you'd then need to choose an appropriate aperture. Most lenses tend be be sharpest at around f/8 and if you needed a larger aperture than f/4 (at 55mm) or f/5.6 (at 200mm) you'd need to increase the ISO sensitivity to achieve correct exposure. Go too high on the ISO and you lose apparent sharpness as the image gets noisier. So it's a dynamic compromise to achieve a fast enough shutter speed to avoid camera shake (motion blur), whilst allowing sufficient light to reach the sensor.