How to prevent blur when taking a photo without a tripod?

No flash, no tripod.
It always blurs on me! What settings should I be using?

I have a Nikon D3100.

Well make sure that you're on "auto" on both the lens AND the base. There are two different switches. But I'm only assuming you're not using manual focus. Also, When you've found something to shoot: Press the button down half way, and you'll see the lenses focusing.

Sounds like you have been using too slow a shutter speed for the lens magnification.

A general rule of thumb is to use a shutter speed at least as fast as the length of the lens. For example, a 300mm lens would need a minimum 1/300 shutter speed. Of course, image stabilization and your own steadiness does affect this number as well.

I would guess you have the camera in fully auto (green) mode? If so, try switching to Tv. This will allow you to set the shutter speed while the camera sets the aperture (FStop). Check your ISO as well, if you are using a low ISO then the camera needs much more light to record an image and even a brightly lit day could result in slow shutter speeds being needed to capture enough light.

What preset camera modes actually do: http://photography.about.com/od/camerabasics/ss/camerapresets.htm
What is shutter speed: http://photography.about.com/od/camerabasics/tp/Shutter-Speed-Photography-Lesson.htm
What is aperture: http://photography.about.com/od/camerabasics/ss/Aperture.htm
What is ISO: http://photography.about.com/od/gloss3/g/FilmSpeed.htm
How to hold a camera: http://photography.about.com/od/takingpictures/qt/howtoholdacamera.htm

Shoot using high shutter speeds, 1/1500th second or faster. Depending upon the lighting, you will have to adjust the ISO on the camera to make that happen

Without any examples we're just guessing. A high shutter speed will eliminate any shake on your part and, to a certain extent, movement on the subject's part. IT will not cure bad focussing.

Use aperture priority and set your aperture, half press the shutter and the camera will tell you what the shutter speed needs to be to get a good exposure.

If it's too slow to hand hold, do any or all of the following,

Raise the ISO, and accept the noise

Open the aperture wider (smaller f number) and accept the narrower depth of field

Increase the light (use flash or wait until the light is better).

Don't use telephoto lenses, use a shorter focal length and get closer to your subject (distance from subject increases the effects of camera shake).

Don't use live view, you'll never hold your camera steady at arms length, even with all of the above.

Buy and use a tripod the above is why photographers use them.

Shoot with higher shutter speeds. Find out how you can increase the ISO settings on your camera, the higher it is the less chances of blurring.

Apart from that, hold the camera still:
Sit and hold it on your knee if possible, or press it against your body.
Hold your one hand under the camera to steady it, close to you body with your elbows against your body.
Press the shutter smoothly, while you are breathing out.
It is amaxzing how slow you can go with the right technique!

It will also help if you have a fast lens. Most wide-range zoom lenses are slow.
People seem to care more about zoom range than wide aperture nowadays. It is a compromise.

Use a wall or some flat level surface, use the camera's self timer to fire the shutter so you don't have to touch the camera.

You could bump up the ISO, but the higher the ISO the more noise you will get, or just use a faster shutter speed and wider aperture. Or a combination of all three.

If there's not enough light, the best way is to use a tripod, or just get more light.

Question/Comment: "How to prevent blur when taking a photo without a tripod?"
Answer: Hold the camera steady, use a fast enough shutter speed, use a faster iso setting.

Q/C: ""It always blurs on me"
A: Please see above.

Q/C: "What settings should I be using?"
A: Depends on what you are taking a picture of. See above.

Q/C: "I have a Nikon D3100."
A: Read the manual. I also recommend taking a photography class or getting a book on photography from the library. It will explain why you get blurry pictures.