When shooting in low light situations finding as much light as possible is crucial. When shooting inside my house, I typically look for north-facing windows. Other windows can be good to—just watch them during the day and look for times when no direct sunlight is streaming onto the floor. I am also a fan of opening up curtains and blinds to let in as much light as possible. Finding the light when there is little light available is a skill and will take time. So open your eyes and look for the light. You can also let light into your camera buy using an open aperture like you find on a fixed aperture lens (50mm f/1.8 or 35mm f/1.8). Be careful not to let more light in by lowering your shutter speed so much that your photos become blurry. Try to keep your shutter speed about 1/125 or higher if photographing kids in low light. You may be able to go a bit lower than that IF your subject is still.
This seems to go against the grain when shooting in low light, but getting your exposure right and then slightly overexposing it will make the grain/noise less noticeable in your images. Any time you have to lighten a high ISO image–even slightly–grain/noise will become very obvious.
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