There are many experienced members here who will be glad to help you improve your photographic skill. Post your pictures and ask specific questions and I am sure you will get very useful answers.
Camera shake can be reduced by using a faster shutter speed. The general guideline is to use a shutter speed no slower than the inverse of the focal length you are shooting at. For example, if you are shooting at 100mm, use a shutter speed faster than 1/100 sec, thus in most cameras, 1/125 sec would be the minimum you should use.
The only way to improve is to learn about the correct method of shooting AND lots of practice.
I have a friend who was having the same problem as you, and he was pretty new to digital photography as well. For your case, I assume you've been using the Auto mode? If that's the case did you remember to activate your flash? The camera won't pop out the flash automatically, so you gotta do it yourself. My guess on why you've been having shakey pictures is because the camera is shooting without hte flash, hence it used longer shutter speeds to allow more light to get captured to compensate the lack of a flash.