Short answer is you can copy database from one computer/server to another using ssh or mysql client.
You can run all the above 3 commands in one pass using mysqldump and mysql commands (insecure method, use only if you are using VPN or trust your network):
$ mysqldump db-name | mysql -h remote.box.com db-name
Use ssh if you don't have direct access to remote mysql server (secure method):
$ mysqldump db-name | ssh email@example.com
You can just copy table called foo to remote database (and remote mysql server remote.box.com) called bar using same syntax:
$ mysqldump db-name foo | ssh firstname.lastname@example.org
This will not just save your time but you can impress your friend too
. Almost all commands can be run using pipes under UNIX/Linux oses.