Is there an easy way to copy one database to another
for large database you need to use command line to (clean) dump local database and after that in remote server to import (with ssh connection and also command line mysql-import or directly after connect to mysql), you need to sepcify your environment (windows, mac..)

some sources:

-http://dev.mysql.com/doc/refman/5.0/en/mysqlimport.html

-http://www.lullabot.com/blog/importexport-large-mysql-databases