There are three main causes of blur:
1. Not properly focused;
2. Hand/Camera shake, your shutter speed is too slow to stop the camera from moving; and
3. Subject Motion, your subjects are moving too fast for the shutter to stop the motion.
For starter, shoot using the 'Rule of Thumb' for your shutter speed. The shutter speed should not be lower than the reciprocal of the focal length. So if you're shooting with a 50mm lens, then your shutter speed should not be less than 1/50 of a second. If you're shooting a 200mm lens, then 1/200th, et cetera.
The Rule of Thumb will take care of blur caused camera-shake.
The next thing to consider is the motion of the subjects. If the subjects are sedentary, then you're okay with a shutter speed based upon the Rule of Thumb. If your subjects are moving, then you gotta up the shutter speed to compensate for the motion. The quicker/faster the motion, the higher the shutter speed. Walking type speed you can get by within a range of 1/60 to 1/125+. For something faster like dancing then 1/125 to 1/250+.
The 1/60 for walking and 1/125 dancing are really on the low end and requires panning with the subjects and waiting for the peak of action to minimize blur. For a new person to photography, it is always better to overcompensate with a higher shutter speed and as your photography progresses, you'll pick up low light shooting techniques.
Start with the Rule of Thumb as a baseline, then adjust upwards to accommodate subject speed. You attain a proper exposure by opening up the lens aperture, or with adjusting the ISO upwards to 800, 1600, 3200 et al ... or you do both, open up the lens and adjust the ISO.
All these setting interact with each other and the image, I've tried to keep it simple. (Remember that the higher the ISO goes the greater the degradation (noise) of the image. The larger the aperture of the lens, the less depth of field ... and so on.)