How to get the bokeh effect with my nikon d3100 with the standard lens?

I want to learn how to blur backgrounds better. I also have a 55-200mm af-s lens.

If you have the space, switch to the longer lens and shoot wide open.

It's critical that you focus on the eyes in portraiture, though.

Three things will result in a shallow Depth-of-Field (DoF), what you call bokeh.

1. The closer the subject (i.e. The closer you focus), the shallower the DoF
2. The longer the focal length, the shallower the DoF.
3. The larger the aperture of the lens (smaller number), the shallower the DoF.

All three things work in conjunction with each other.

Of the three, the focal length is the most significant, and trumps all other settings. In fact if the focal length is too short - everything will be in focus to infinity regardless of what your subject distance or aperture is set to.

So if you are using a zoom lens, always use the longest focal length you can get away with and still keep your subject framed.

First, zoom in (towards the Telephoto end) as much as you can.

Next, move your subject as close as you can to the camera, while maintaining the ability to properly compose the photo. It would help also if the background is some distance. There may be some tradeoffs here between focal length of the lens and subject distance, but favor the longer focal length as much as you can.

Finally, set the aperture to the smallest number (widest opening) you can.

You may have to trade off one of these items to get the best combination, but hopefully you will at least get some hint of a blurry background.

But what if you don't have a fast lens?

It is little known fact that a 200mm lens at f/5.6 may give superior DoF to even a 50mm lens at f/1.8.

I shot this photo with a 18-200mm lens at 200mm and f/5.6, which shows you don't necessarily need a fast lens if you can use a telephoto lens: