The question is extremely broad. There are a lot of questions and answers here that address particular aspects of blurry pictures. Putting all of that in one answer would be excessively long as well as redundant. I've grouped many of them under different headings and provided links to other questions and answers here at Photography SE.

Is your camera moving during the exposure?

Probably the number one reason for blurry pictures is camera motion. The sharpest images are those taken with the camera immobilized on a solid mount, usually a tripod. That isn't always possible, though. When shooting with the camera handheld good camera handling techniques and proper shutter times are vital.

How much does a camera move in 1/250 of a second?
At what shutter speed threshold does a tripod start to matter?
How can I determine the minimum shutter speed to avoid blur from camera shake?

Image Stabilization can help with camera motion in certain situations, but IS/VR/VC/etc. has limits to what it can do.

Is your subject moving?

This can affect your shot in two ways:

• The AF system may have difficulty tracking a moving target and the focus is missed.
• The subject motion may be significant enough during the exposure to allow blur.

IS/VR/VC/etc. does nothing for subject motion.

Why my "action" shots are blurry even shooting on AF-C, is this a lens or camera limitation?
Focus problem vs. motion blur vs. camera shake - how to tell the difference?
What went wrong with this concert photo and what could I have done to make it better?
How can I avoid this blur during taking indoor party pictures?

Are you giving your camera's AF system enough light/contrast to focus?

PDAF (viewfinder) and CDAF (Live View) both require contrast to successfully focus your lens. If the combination of low light and a narrow lens is pointed at something with low contrast, the AF system won't perform well, if at all.

What could be causing focus problems in low light?
How can I focus quickly outdoors in the dark?

Are you really telling your camera to focus where you think you are?

The camera may be focusing exactly where you told it to focus instead of where you thought you told it to focus. Just because you think the camera is missing focus doesn't mean that is what is causing blurry pictures: How can I more consistently focus on the point I want?

With pretty much any modern AF system the areas of actual sensitivity are larger than the little markers for each AF point that you see in your viewfinder. The good news is that each one covers a larger area than you think. The bad news is that each one covers a larger area than you think. If your target is very small but there is an area of even greater contrast within the area of sensitivity, the camera will almost certainly focus on the area of greater contrast. For a look at how this works out practically when shooting, see this entry from Andre's Blog. For a look at how AF accuracy can vary from shot to shot, see this entry from Roger Cicala's blog at lensrentals.com.

Although there are a lot of similarities between various PDAF systems, they all have their own "map" of areas of sensitivity for each AF point. They all have different degrees of sensitivity for various AF points and maximum lens apertures. In order to master any of these AF systems, practice is required! It's not enough for you to know where you think you are telling the camera to focus. You have to learn to speak the camera's language and see the scene in the viewfinder the way the AF system does.

How can I effectively use the focus points (of Canon DSLR), to get accurate focus on a small subject?

Is your lens focusing where the camera told it to?

Sometimes slight front or back focusing issues caused by the manufacturing tolerances of the camera and lens match up fairly well and they cancel each other out. At other times they compound upon each other. Autofocus micro-adjustment can help to match the lens to the camera. Be sure you're doing the testing and adjustment correctly, though, or you can make things worse.

Do the issues with sharpness I am seeing require AF fine-tuning?
Which offers better results: FoCal or LensAlign Pro?
What methods can be used to micro-adjust autofocus of a camera body to a particular lens?
Does this test chart show that my kit lens front focused?
Fine tuning a lens focus

Are you using best technique and AF practices in challenging shooting environments?

I'm having trouble getting sharp pictures while shooting a concert from a press pass location
How do I reduce blurriness when shooting dancers on stage?
Why isn't my DSLR focusing accurately on a fast-moving subject?
How to focus on fast moving objects with a low-end dslr?
Canon 7d & 24-70 ii - can't get a crisp or well exposed shot

Are you sure the photo is blurry at all?

Sometimes other issues, such as improper exposure or poor white balance settings can make a properly focused image look blurry. Fixing the exposure or WB can often show the image was more infocus than it first appears. In challenging light be sure to save the raw data, it can allow you to draw out more detail than an in-camera produced jpeg will begin to show.

Blown out blue/red light making photos look out of focus
How to cancel purple stage lighting on subjects?
Lots of noise in my hockey pictures. What am I doing wrong?

Have you reached the limits of your camera/lens' capabilities?

How can lens cause consistent front or back focus?
How can I effectively use the focus points (of Canon DSLR), to get accurate focus on a small subject?
Does autofocus work better with f/2.8 lenses vs f/4 or slower?
Canon 24-70mm 2.8f - Optimal aperture for sharper pictures
How can I best utilize a point-and-shoot for concert photography?
Why is in-camera stabilization not popular?

For more regarding various causes of blur in photos, please see:
What causes blurred/non-sharp images taken of stable objects?
Why are my football action shots blurry?
How could I achieve stock quality sharpness?
Why are my photos not crisp?
If the focal plane is curved, should the outer AF points work correctly or front-focus?
Blurry pictures when zooming in