how to move a database to a new server?

[Andrew Pasetti]

Can someone please recommend the easiest way to transfer a database (with data) from 
one server to another? Here's the server info: 

Existing server: 
Linux 2.2.14-5.0 running mysql 3.23.10-alpha 

New server: 
Linux 2.2.14-5.0 running mysql 3.23.32 

Thank you. Your feedback will be greatly appreciated. 

--Andrew