How can I adjust my camera for non-blurry, natual light photos?

I like to not use the flash and love the look of natural light photos, but I am having trouble with very blurry images (camera shake). I dont want to have to use a tri-pod, as I am taking pictures of children, etc. Is there any setting on my camera that would help with this?
Thank you for any advice

Honestly, James DeRuvo definitely answers this question the best, so I'll put in what he normally tells people in this situation:
"Other ways to increase performance are:

2. Use faster SD cards. Yes, there are faster cards and it does make a difference in writing the image file to the card. This is especially key if you're taking multiple or burst images.

3. Fresher batteries. Use alkalines at least. But I recommend using high energy batteries designed for digital photography. Varta is a good brand. They are usually sold in camera shops, are long lasting (because they are sold in small quantities) put out alot of energy.

4. Pan with the action. You can create some pretty cool shots by panning with your shot, focusing on your subject. This will create the effect of your subject in sharp contrast to the blurry background.

6. Stick with 100-400 ISO. Going higher will cause more noise/grain in your shots, particularly in darker settings.

Doing these, particularly prefocusing and panning with the action will cut your shutter lag by as much as 80%."

Hopefully he doesn't mind me quoting him, but quite frankly this is the best way to go about it.

Try setting your camera in the (A) aperture mode to the lowest numerical setting. If this doesn't work, keep the setting and increase your ISO to 200 and if this doesn't work go to ISO 400 etc. until you get what you want. As you go beyond ISO 400 you may start seeing some noise in your pictures. Check reviews for your camera and you can find out how high you can go with the ISO before picture quality deteriorates.

Actually my previous answer was not the best. Set your camera to the (S) shutter priority mode. I am not familiar with the shutter speeds of your camera, but try something around 250 and go up from there until you lose the blur.

With a nice camera like the Nikon D40 you should check out photography courses in your area, and then you can enjoy all of its great capabilities.