Preventing or Reducing Camera Shake
There is a style of impressionistic photography that involves intentional camera shake. But most of the time, it's best to keep things steady while shooting to prevent or minimize camera shake. Depending on the situation, there's more than one way to cure the shakes.
Your first line of defense against the marauding onslaught of camera shake, that scourge that robs your images of sharpness, is your tripod. Indeed, some tripods are so big and heavy that they could be offensive weapons as well, but that's really the point. You want a tripod that is massive enough to remain still when a light gust of wind strikes. No, a gust of wind doesn't sound that bad, but depending on what lens you are shooting with, it could spell disaster. Extreme telephoto and macro shooting both demand stillness. Many professional cameras have a feature to lock the mirror up to prevent mirror slap from causing a vibration. Any slight shudder could register when the shutter fires if the image is magnified enough. All you mirrorless users are one up on me as I'm still shooting with a DSLR. But there's no denying that this is a clear advantage of ditching the mirror.
But while you can dispense with the mirror entirely or lock it up out of the way to keep it from moving, other sources of vibration can be harder to manage. A big enough tripod would sufficiently dampen most external vibration, but carrying such a beat around can be a pain, literally. Besides solving camera shake, the most well-known use of a tripod is to help build powerful shoulder muscles. But if we give in and leave our tripod at home, the camera shake could win, and so we persevere. Carbon fiber was a godsend when it first started seeing use in tripods from Gitzo more than twenty years ago. It didn't get cold like aluminum did in winter, and it shaved enough weight off to let us feel comfortable that we were doing all we could. But even now, don't assume you can own one tripod suitable for all occasions. The heavier the load, the heavier the tripod you will need. With lighter gear, a travel tripod or monopod may suffice.
With a short enough focal length to ease worries about magnification, it's possible to hand-hold your camera, but be careful. There's an old maxim that you can safely hand-hold at shutter speeds faster than one over the focal length. So if you're shutting with a 50mm lens, the rule says you should be able to hand-hold your camera so long as the shutter speed is faster than 1/50 second. But today's higher-resolution sensors can be unforgiving. Pay attention to your technique, and if you expect to get the most out of those megapixels, do some testing to establish the limits for yourself. Or deduct an extra stop by dividing the formula estimates in half. Better safe than sorry.
Some guides will recommend shooting with a faster shutter speed to minimize shake. I don't see this as a viable option in most cases. Doing so might lead to a reciprocal change to aperture to maintain the same exposure. But this would directly affect the visual depth-of-field.
Thankfully, modern cameras have improved in more than just resolution. Newer cameras have markedly improved their high-ISO performance compared to those sold only a few years ago. You man find that bumping the ISO will allow you to get excellent results with shorter shutter speeds. If you can take the picture before your camera has time to move, you'll avoid much of the motion blur problem. Don't use high-ISO as an excuse to get sloppy, but also don't discount ISO as a tool to minimize shake.
Then there are vibration-reduction lenses, and in a few cases, vibration-reduction camera sensors. In both cases, the concept is the same. Gyroscopic sensors detect the motion and move either a lens element or the sensor itself against the movement to compensate. Vibration reduction, also known as "image stabilization," "anti-shake," or other names depending on the vendor, can gain you several stops when compared to the "hand-holding" rule. Read the particulars of your system to understand the details. Many require you to disengage the mechanism when shooting from a tripod. Also, be careful not to leave it on all the time. If you can already safely hand-hold, skip the VR feature. And always turn it off before putting your camera away. The mechanism is delicate. A sudden jolt can damage your lens inside your camera bag if you leave the VR engaged.
Shoot most images with a remote shutter release. There's no sense in nudging your camera by pressing the shutter release if you can avoid it. Some cameras use cabled releases, others infrared. Both can be a bit of a nuisance to use, but it makes to do so. Consider it another way to slow your process down and improve your craft. Attention to detail can help you get better images.
It may not be evident that camera shake is the problem. If you look at a soft image, you may be tempted to blame the lens. Or perhaps the focus was way off. The shutter click for a typical image is so short it doesn't seem the camera would have time to move. But it doesn't take much.
Of course, sometimes the answer is far more straightforward. If you find yourself on one of those mornings when you just can't wake up no matter what you do, maybe you've just had too many cups of coffee. That could give anyone the shakes. Don't ask me how I know.