Essentially you want to do something very similar to this on the server you want to EXPORT data from:
mysqldump -u user -ppass -h host databasename > export.mysql
You can remove -u, -p, -h depending on where your server is and your mysql.cnf
On the server you want to IMPORT the data on you do this:
mysqldump -u user -ppass -h host < export.mysql
You can get fancy, and do --add-drop-table, and that will drop tables if you already have the structure before adding the new ones.
Look at the mysql documentation online (www.mysql.com) it's good.
Jeff