How to take a good quality photo in the dark without using flash on a dslr?

I have a Nikon 3100

I've never had a Nikon but i'm pretty sure it has a switch for Night time on it just like Canon's.
Thats should give you a better quality photo, if not you will just have to light the focus using something else lik a light behind you and such.

In the dark you get no picture.

Two alternatives:

Use a fast prime lens. That will enable you to open up the aperture far wider than your standard zoom, thus letting in much more light. This will help to keep the ISO at bearable levels, or to shoot at high ISO values in situations in which you wouldn't be able to shoot otherwise.

If your subjects won't move or motion blur even is desired, then you can do a long time exposure. For that you don't need a special lens but a tripod, and you can even keep the ISO down at normal daylight levels.

Use a tripod and long exposure. If your subject is not likely to move (or will move so fast you could not freeze its motion anyway), use low ISO and more exposure rather that turning up the ISO. High ISO causes noise, and at low light levels the problem is even worse.
Focusing the kit lens can be a problem if the light is very low. You may need a flashlight to illuminate something, or you may need to find something bright on the horizon. If that is not in the spot in the scene you want, you could try pre-auto-focusing, and then switch your focus from auto to manual. Then do not change the focus or the zoom. Changing the zoom may change the focal point.
For exposures longer than 30 seconds use bulb and the optional remote.

For slow shutter tripod shots use the remote, or give it at least 5 seconds of time delay. That will allow vibrations to settle down.

Get your Nikon3100, put the lens cap on it. Buy a carrying bag. Put the camera in the bag. Sell the camera. Buy a Nikon D3x or D3s. Problem solved.

Use a flash system off the camera. That will produce much better results than flash on the camera.

Low light photography without flash, you need a fast lens. The 35mm and 50mm f/1.8 AF-S lenses work well for low light photography.
Tripod is helpful.
Using higher ISO settings helps, but you start increasing noise past ISO 800.
Remote trigger is also helpful to reduce camera shake.