Blur is usually caused by missed focus, camera movement or subject movement, or any combination thereof. [[2nd edit to add crappy lenses as another cause]]
To combat this, I tend to use a minimum shutter of 1/250 (to combat movement) and f4-8 depending on my focal lengths (4 on shorter lengths 35-50 on a crop body and 8 on the longer like 135-200) to give me a little more wiggle room on depth of field. Way down at f2 and below I can easily focus on eyebrows and even eye lashes and miss the eye. Natural gloomy light can be an issue, so sometimes I'll drop to 1/125sec but anything slower and my hit rate gets disproportionately lower because of camera/subject movement. Anything lower than 1/125 & f4 and I'll always push ISO. Occasionally I'll have fun at f1.2 - 4 but the amount that gets binned (esp at 1.2) is silly.
The problem is that different people have different steadiness, different versions of image stabilisation (or none at all), different available apertures and different preferences for focal lengths. All of these affect "blurriness" in images unfortunately, so there's no real "one size fits all".
Edit to add: Using strobes massively improves hit rate. Being able to shoot at f11 & 1/250 means I almost never get a blurred shot. Consider artificial help perhaps?
