Most tethering softwares that list support for Nikon cameras do not include the D3xxx series. Most of the Dx, Dxx, and some of the D7xxx and D5xxx bodies are at least partially supported. The D3100's firmware or hardware may limit this capability.

If all you want to do is view the output of your camera without controlling it, you just need to connect it to a device that accepts an HDMI input. The easiest and most economical solution would be a display only device such as a portable HDMI monitor. Most laptops do not accept HDMI inputs due to copyright constraints on the licensing of the HDMI technology. Alienware once made a couple of models, the M17X and M18X, that would do this, but they were very expensive. Dell, who bought Alienware, still lists the M17X and M18X with HDMI-in capability. They're still very expensive. There may be other models that also do this. Be aware that according to page 42 of your D3100's user manual:

When the camera is attached to an HDMI video device, the camera monitor will turn off and the video device will display the view through the lens as shown at right. Movies can not be recorded and photographs can not be taken in live view while the camera is connected to an HDMI-CEC device

If you are willing to drop down to standard video quality using the TV out port on your camera, a USB video capture device will allow you to display photos from your D3100 on any laptop with a USB port, but you would not be able to view the live view output this way, only captured images or video.