Once you have taken a mysql dump you may want to transfer this to another server. You can do this using scp (secure copy).
scp [database name].sql [username]@[servername]:path/to/database/
scp dbdump.sql luke@x.x.x.x:~/
The example above securely copies the db to the server x.x.x.x and places the file in the root directory. (note: you will need to enter the password for the destination user/server)
scp -P 666 filename.sql user@x.x.x.x:/