Hi,
If the control panel on your old server is supported by plesk migration utility and you have root or sudo user there, the best way would be to use the Plesk Migration tool. You can find instructions for it at
http://download1.parallels.com/Plesk/Plesk8.2/Doc/plesk-8.2-unix-administrators-guide/17348.htmIf the old provide also uses Plesk on Linux, you can simply backup your accounts there, upload to the new server and restore there.
If no of the above condition apply, I'm afraid you will need to re-create all the settings and re-upload data for the sites manually. Lunarpages staff can also assist you with that for $75/hour fee.
Please advise if you have any further questions or concerns.