You can spend a lot of money and a lot of time trying to "degrain" your pictures, but you should consider the source of the issue, which is the shooting conditions and the camera.
First, the shooting conditions. Low light conditions are difficult for cameras just like they are difficult for our eyes. Our eyes and cameras need lots of light to see. If there is too little light, then our eyes maybe can't see. But, the camera can cheat (at least for a certain amount).
The camera can cheat by raising the ISO, which is essentially boosting the gain on the electronic signal. If you don't know that means, think of a bad radio station -- one that you are barely getting in on the radio, with lots of static. You can barely hear the song over the static. You can turn up the volume, but the static turns up at the same time. Maybe you can more clearly make out the song lyrics now, but the static is even more annoying. That's one way your camera can cope -- it can raise the ISO, but at the same time, you'll get more static (that is, noise or grain).
Two other ways the camera can adjust for low lighting -- one is by increasing the size of the aperture. Just like our eyes, the camera has a pupil called the Aperture. The bigger that pupil is open, the more light that comes in. Our eyes' pupils open wider automatically in darker conditions. Camera's can, too. How wide it can open is dependent on the camera. There are also trade-offs to opening or closing the aperture more, but I'll leave that alone for right now. Suffice it to say, the darker the conditions, the more open you might want the aperture, but your camera is probably trying to go as wide as possible, anyway.
Another way for the camera to adjust is to lower the shutter speed. The shutter speed is the length of time the shutter opens to let in light. This is a bit different than the way our eyes work. Our eyes are more like movie cameras -- always taking in images. A camera captures an image frozen in time. The longer the shutter is open, the more likely the subject will move during that time, and the more likely the subject will be blurred. For kids, anything below 1/60 second will likely look bad (unless you are going for an effect that shows blur to demonstrate movement). 1/125 second and higher is preferred.
In low light situations, if you're camera is on automatic, the camera will try to get as fast a shutter speed as possible. This means it will open the aperture as wide as it can, and will raise the ISO as high as the logic in the camera allows. Even then, it might not get a high enough shutter speed to "freeze" your subject.
So, there are two other things you can do.
1) Get more light. Just like our eyes, the camera needs more light to get really good pictures. This might mean turning on more lamps, or it might mean more flash. However, many people really want to take more "natural" looking photos in what you would call "available light", so that leads to solution #2 which is
2) Get a different camera (!). I am guessing you are using one of the many, many, many models of consumer-level pocket cameras. (Let us know which camera it is). Have a look at this link:
http://en.wikipedia.org/wiki/File:SensorSizes.svg
Do you see in the lower right corner, where it says 1/2.5"? That is likely the size of the sensor in your pocket camera. Have you heard of a DSLRs? Look at the second row, where it says "APS-C" (Canon or Nikon -- they're close enough). That is the sensor size in the typical consumer-grade DSLR (the larger sensors are getting towards pro level). As you can see, the APS-C sensors are, what, ten times bigger than the 1/2.5" sensor? That means much more light gathering ability for the same shot! What this means practically is that if you have the same aperture and the same shutter speed, the DSLR ISO's (remember the signal gain) can be boosted much higher before you see noise/grain. My Canon DSLR can make shots at ISO 1600 that look better than my Canon pocket camera at ISO400. This means (if the aperture is the same), I could take a picture on my DSLR at ISO 1600.
If you want to see just how different, go to this site, and choose "Canon SD1000" and "Canon D1000" to compare a pocket camera (SD1000) to a DSLR (D1000). Compare the ISO800 pictures on both, and your jaw will hit the floor over the difference.
If you want to learn more technical stuff, you could visit a site like this one:
http://www.cambridgeincolour.com/tutorials.htm or buy a book like Understand Exposure by Bryan Peterson.
That's the long answer and the background. Here's the short answer; you can try to "de-noise" your picture, but you'll likely spend a good amount of money and a lot of time to find this simple truth: you can only remove so much noise before the picture really starts to lost detail and look more like an impressionist painting than a picture. So, you need to either a) add more light for your camera, or b) get a different camera with a bigger sensor.
You could also help yourself if you learned how to balance shutter speed, aperture, and lighting.
but deciding that criteria and making adjustments is inherently manipulating a negative to a final vision you intend of it. It's all manipulation. Some is just more extreme than another. Even deciding to shoot in color or black and white is manipulating the scene in front of you. Photography IS manipulation.
