You have probably experienced shooting blurry photos usually as a result of wrong camera settings or the object moving while you were taking the photo. Such blurriness is not something you would like to see in a photo but if controlled some blurriness can actually be used to capture and convey the feeling of motion in a still photo.
Shutter speed is what determines if a photo is frozen or blurry. The faster the shutter the more frozen the photo is. The slower the shutter the more motion is captured in the photo in the form of blurriness. Open the shutter for too long and the photo will be completely blurred.
There are two ways to capture motion: to blur the moving object while keeping the background in focus or to blur the background while keeping the object in focus:
Blurring the object: Blurring a moving object captures its motion. For example consider a car driving down the road. If you freeze such a scene with high shutter speed the viewer can not tell if the car is moving or if it is parked. However if you use a slower shutter speed the moving car is blurred and the feeling of motion conveyed.
Blurring the background (panning): Consider the same car from the above example. Another way to convey its motion is by blurring the background while keeping the car in focus. This is much harder to accomplish. The concept is simple: set the camera to a slower shutter speed. Pan the camera in a way that it follows the car. The car stays still at the same spot in the photo. Then shoot the photo as you continue panning the camera to keep it aligned with the moving car. The result is a car that is in focus while the background is blurred.
What is the right shutter speed needed to capture motion? Unfortunately there is no magic number. The shutter speed depends on many factors such as the speed of the object, its distance and the amount of motion (or blurriness) that you would like to capture. As a rule of thumb shutter speeds faster than 1/250 of a second tend to freeze the scene while shutter speeds slower than 1/50 of a second tend to result in some blurriness. If the object is very slow you might need to keep the shutter open for even a second or more. If the object is very fast 1/50 of a second can be all that you need.
It is very important to keep the camera steady when taking photos using slower shutter speeds. Usually when capturing motion in such a way you would need to stabilize the camera using a tripod or by putting the camera on a steady surface. The exception is when trying to blur the background of a moving object – since you need to pan the camera to keep it aligned with the object the camera inherently needs to move. The movement needs to be in the same speed and direction as the object and only in that direction. Sometimes such panning can be done using a tripod that allows control movement of the camera.
Photos that capture motion are impressive. The only way to learn how to shoot such photos is by experimenting. Start with experimenting blurring the moving object. This technique is relatively easy and within a short time you will master it. Once you do try to experiment with blurring the background. This is much harder to achieve and can be frustrating at the beginning.