Migrating is fairly simple if you follow these steps:
1) Create your mailboxes in the Zimbra Control Panel
2) Set up your email application
3) Export old .PST then Import your .PST file(s) to your new hosting company
4) Modify your DNS records
I understand these answers are simple, but there really is no need to over think it. These are the instruction, generally, that where given to me when i migrated to a new company that hosted Zimbra called The Message Center.
Very good hosting company.
The Message Center Hosted Exchange, Hosted CRM Hosted SharePoint, Hosted Zimbra