There are a number of ways to do this.
One is to use a ready made application that will synchronize data between databases. Another one is to create an application yourself....which may be difficult...depending on what you are trying to achieve....etc.
Have a look at webyog...I believe it offers database synchronization between remote and local mysql databases. I think the community edition is available for free....
Also, you should have a look at PHP Classes from http://www.phpclasses.org
here is a class that performs schema synchronizations