Cleaning a saxophone will not only help it produce a clear tone but will prolong its life as well. A straight saxophone, such as the soprano, requires special tools to be properly cleaned. However, most other bell shaped saxophones can be cleaned quite easily using a standard cleaning kit. The information here addresses the more common bell shaped sax.
Clean the mouthpiece by removing the reed and ligature and running cold water through it. Then pull a clean lint free cloth through the mouthpiece to dry it and remove any particles the water missed.
Clean the valve pads by sliding a piece of paper or pad cleaner underneath the pad. Then close the valve and slowly pull the paper out. If a valve pad is torn, don't try to replace it yourself. Take it to your local repair shop and have a professional take care of it for you.