Most digital cameras suffer from shutter lag. There’s a delay between when you press the button and the photo is captured. It is possible that your subject could move, causing blurriness. But I doubt that is the problem.
First, make sure you’re not causing the problem. Brace your arms against your chest when you take photos. Stand with your legs shoulder width apart. This will help reduce camera shake. But positioning yourself correctly is only part of the solution.
The problem could be situational. In low light, shutter speed is slower; this lets the sensor collect more light. If possible, increase the ambient light. Or, use the camera’s mode for low lighting. You can also increase the ISO. This makes the camera more sensitive to light. It will speed up shutter speed and decrease blurring. But remember that higher ISO settings cause more noise.
You can also use a tripod and remote shutter release. That way, you won’t shake the camera while the shutter is open. But, obviously, a tripod is not appropriate for candid shots. If problems persist, consider exchanging your camera for one with vibration or shake reduction. This isn’t a silver bullet, but it can help.