Do you have access to phpMyAdmin at the source server? If so, phpMyAdmin can export databases and tables that can be imported at the target server by a simple mysql_query().
If phpMyAdmin is not installed, you can write your own queries to export data as SQL input to an update at the target.
If you have FTP access, you can copy the files. A MySQL database is just a directory containing files, 2 or 3 per table depending on file type. Just download from one machine via FTP then upload to the other. (FTP does not give you the chance to cange from older format MySQL files to newer file types.
If you are stealing information from a database at the CIA and all you have is a HTML display of the data, it is possible copy & paste the data in to an editor, like PFE, then save the file as text and either use the editor commands to reformat the data to a readable file format or use PHP to reformat the data. Just do not call the CIA Help Desk and ask them to help you. :-)
mySQL allows LOAD DATA INFILE, something that lets you set up a text file as input to an SQL statement and the SQL statement acts a bit like a template for the fields in the file. Have a look at MySQL\'s documentation on \"load data infile\"
