SSH to the server where your data is located, and run these commands:

1. cd /PATH_TO_DATA_DIRECTORY
   Assuming that your data is zipped in *.tar.gz format:
2. /usr/bin/scp -P 22 *.gz root@IP_ADDRESS _OF_NEW_SERVER:/PATH_TO_WHERE_DATA_SHOULD_BE_SAVED

For example, let's say you're transferring your client's data from ThePlanet to ServerTune, you'll run this command:
/usr/bin/scp -P 22 *.gz root@70.69.12.34:/backup/cpbakcup/daily/