Hi I find my shutter speed is slow.. I take a picture of a slow moving object and by the time the photo is taken, the object has moved out of frame

The most likely culprit is a slow shutter speed. If the subject moves while the picture is being taken, you'll see it blur. If non-moving objects show up sharp while the moving objects are blurred, then this is definitely it.

Another possibility is camera movement. Try putting the camera on a tripod or a table or other steady support, then use the self-timer to take a picture. If everything in the picture is blurry, then this is probably the reason.

The third possibility is that the camera isn't focused on the subject. Try taking a picture of the subject when it isn't moving and see what happens.

There are several possible causes for blurry pictures.
1) Camera motion. If everything is blurry, it's most likely because the camera moved while the picture was being taken. Make sure your shutter speed is fast enough if you're handholding the camera (longer lenses require faster shutter speed). Alternatively, put your camera on a stable surface, such as a tripod or a tabletop.
2) Subject motion. If the subject is blurry but the background is sharper, then the subject may have moved while the picture was being taken. Use a faster shutter speed. Raise the ISO if needed. There are limits, of course. If you're trying to photograph a fast-moving object in the dark, you probably won't be able to.
3) Improper focus. If the subject is blurry but something else in the picture is sharp, then the camera probably focused on the wrong object. Move the focus selector to the subject you want in focus. Alternatively, center the viewfinder on the subject, press the shutter button halfway to lock focus, then reframe and shoot.
Without any more specific information as to what and how your pictures are blurry, I'm afraid the above is all I can give you.

What mode are you shooting in? It seems you may either have your shutter speed set manually to a slow speed or, alternatively you have set your apperture set to a high number e.g f/20 or there abouts. Because this is a very narrow apperture the camera will compensate by using a slow shutter speed.
Try some shots in fully automatic mode and see what happens. With a slow shutter speed you can expect any movement to produce blurred images.

If everything in the picture is blurry, you are moving the camera when you press the shutter button. If only the subject is blurry and the background is clear the problem is too slow shutter speed. If this is cause by movement of the camera you must learn to SQUEESE the button while being sure you don't move the camera. It just takes a little practice. If this problem caused by a shutter speed that is too slow, it is remedied by increasing the ISO "film" speed. Even though you have no film, the camera has a "speed" setting that relates to that. The higher ISO value increases the camera's sensitivity to light and thus allows for faster shutter speed. Normally the ISO choices are 100, 200, 400, 800, 1600. Try using 400. The ISO setting is in one of your camera menus. 400 is fast enough to solve your problem in all but very fast movement of either the camera or subject. Using ISO above 400 will cause your pictures to look grainy and not as sharp. Use the highest speed only when absolutely necessary. Slower ISO numbers produce the finest grain and thus the sharpest pictures. It a trade off between ISO and shutter speed because the exposure is a combination of the ISO and shutter speed and lens opening. Each one effects the exposure by half or double.

It indicates the shutter speed is too slow for you to hold it by hand without something like a tripod.
Either there's not enough light in the conditions you're taking the pictures in, or you need to try changing the settings on the camera, such as increasing the ISO setting, or light sensitivity, so it can use a faster shutter speed.
If it's close range, turn on the flash.
If you can't change the settings, you can try bracing your hand against a fixed object so that the camera doesn't move, and just gently squeeze the button to take the picture. Novices frequently jab the shutter release to take pictures, which will cause blurry pictures from the camera moving.

Photographyat night can be used to create mysterious and amazing photos. When I sayphotography at night I mean the hours from around sunset until when the starsare clearly visible. The long exposures associated with low light can createunique effects and unusually sharp photos. And when I say long exposures I meanexposures lasting from half a second up to even 30 seconds. An exposure thatlong would seem impossible to prevent shaking, so my technique that I use veryoften is to compose the photo like I would normally and then to set theself-timer so the camera takes the picture on its own and I don't even have totouch it.
EquipmentOptions For lowlight photos, a tripod (or some kind of substitute) is very necessary. I almostalways keep a tripod in the trunk of my car or carry a miniature tripod aroundon trips. A miniature tripod can be very handy because it is typically smallenough to fit in a pants pocket so it can be taken anywhere. Some photographerscarry around a bean bag or something like it so that can set their camera downand tilt it in any way they like. Some of my best pictures I have taken simplyby setting my camera down on a newspaper stand and setting the self-timer.

Many photographers are convinced that they need a cable release to take longexposures but the self-timer release option on just about all cameras worksjust as well. All you have to do is set the camera up, configure theself-timer, press the shutter button, and wait the specified amount of time(usually 10 seconds) and the camera will take the photo automatically. And youdon't have to touch the camera so the photo won't be blurred from hand shaking.

Night Photo Opportunities
Landscape Photos - My favorite kind of night photousually includes a landscape with some kind of foreground element, some sort offraming element, and lots of lights throughout the scene. Adding some kind offoreground item to the frame helps to create a greater depth of field, thistechnique works for any kind of photo but I have found that it makes nightlandscape photos much better. Another tip you should keep in mind is that themain subject of a night photo should probably be the most well lit. Lots oflight is good for a night exposure but there should still be some focus appliedto the major objects in a scene.
CapturingMotion - A verypopular kind of night photography includes a steady camera with some sort offast moving object streaming through the frame. When cars are photographed atnight with a long shutter speed, the headlights make a bright pathway of lightand in most cases the car can't even be seen. Another option would be to set upyour camera next to a lighted area with lots of people moving like a night clubor an illuminated street. Just about any kind of motion captured with thecamera steady produces a very interesting photo.

Balancing Aperture and Shutter SpeedWhen taking photos at night you should keep aperture in mind as well asshutter speed. It is without question that you will need a long shutter speed,but the aperture that you choose will provide the depth of field. When I takenight photos I usually have a very long shutter speed (5-15 seconds) and a verynarrow aperture (high f-stop). This combination creates a huge depth of fieldand makes everything very crisp and in focus. Of course sometimes you will notdesire a great depth of field and in those situations you should widen theaperture (small f-stop).

Calculating the ExposureFiguring out what exact shutter speed and aperture you should use can bevery challenging in Manual Mode. I would recommend that you just try manydifferent combinations for each scene and eventually you will refine thesettings that you prefer. Another technique I use is Bracketing, if you bracketall your photos so the camera takes multiple exposures at different settings,you are more likely to end up with a photo that has a satisfactory brightness.
Conclusion There is no exact science to night photography; I hope some of these tips willguide you in the right direction. But the best night photographers are usuallythe people who experiment a lot when they are taking low light exposures andeventually they figure out the best scenes and best exposure settings to match.Just remember that you need a very long shutter speed setting, and that youneed to keep the camera very steady.