You got a case of the blurries! And you don't want it. (I concede that there are times you do want a photo to be blurry, but if that's the case then there's no point in reading this section. Yes there is! Your unquenchable thirst for KNOWLEDGE! Keep reading!)
Lots of things can cause blurred images!.
Whoa! Did you see that thing fly by? Did you get a picture of it?
Anything in the frame that moves while the shutter is open will leave a blur. Remember the good old days? Back in 1870? When people had to stand really really still for several seconds to get their likenesses taken? Yeah, that was a bummer. But it was because the shutter was open that whole time, and they'd leave a blur on the image if they moved.
So the solution is to make a faster shutter so that the subject doesn't get a chance to move while it's open.
Sometimes this is easy, like with humans posing for a portait. (Unless they sneeze or are flying downhill on a mountain bike.) Other times, it's more difficult, like with a hummingbird's wings.
If the light is lowish, you can fire the flash even if it's during the day. In this case, maybe there will be some blur around the subject, but the flash will highlight the subject for just an instant, leaving a clear impression.
Other tricks to make a shorter exposure are to decrease the f-number, or increase the ISO. See the Shutter/F-stop/ISO online demo to see this in action.
Not the polite kind, either. How steady must you hold the camera to prevent blurring of the final image? Well, most SLR photographers use a rule of thumb to determine how fast the exposure must be to counteract the effects of a shaky hand...
But the best tips for point-and-shoot types are these two:
You can support your hand with something—another body part, the wall, or anything steady. This will help tremendously.
Also, you can use the "multiple shot" trick. If your camera has a rapid fire mode, turn it on hold down the trigger for three shots or so. The odds are much better that you'll get an image that you happened to be holding steady for. (Especially since the first image tends to be the blurriest with the jostle of the trigger press.)
Is the light too low? This is a variant on the previous issue. If it's too dark, the camera will leave the shutter open for a long time to take the picture, and imperfect humans simply can't hold their hands rock-steady for very long. You can shorten the exposure or use the flash, as previously pointed out, or you can put the camera on a tripod for stability.
Maybe we should have started with the obvious, but: is the camera in focus? Maybe you set the camera set on manual focus mode and you forgot to change it back to auto focus? I do this all the time, and man, it's a pain!
But assuming autofocus is on, is the camera focusing on the right thing? Maybe you have your friend posing in the foreground, but the camera keeps focusing on the background. In this case, point the camera at your friend, hold the shutter down halfway until the camera focuses, then keep holding it down half way, and reorient it to the direction of your shot. You're telling the camera, "first focus on this, but don't take the shot until I say." Once everything is composed to your liking, press the shutter the rest of the way.
Cameras take a look at the scene in a variety of different places to determine if things are in focus or not. Usually there's a little pattern of seven or nine points that the camera uses and does the best job it can to get all of them in focus.
Or some of them. It's up to you—you can tell it to use all the autofocus (AF) points, or just one of them.
This can be very useful if you have your subject on one side of the photo and you really want him or her (or it) to be in focus, but the rest of the shot isn't important. You simply use the one AF point that is over your subject and disable all the rest of them.
I know the million dollar question is how to make your camera do that, but since all cameras are different, the best I can do is coldly refer you to your user's manual.
Is it too windy? Even on a tripod, wind can cause a camera to shake during an exposure. Try shielding it with your body or your coat and make sure the camera strap isn't flapping in the breeze. This probably won't help much. Sorry! Get a beefier tripod, or resort to prayer.