Depends on your host, you might be able to copy the email files themselves via FTP from the source server to the destination server. Alternatively connect to both the old and new host via IMAP using your email client and literally drag the emails over. Either way you need to setup the new email accounts first so you have somewhere to send the emails to. Finally if your new host is any good they'll move your site over for you for free or at least sort this out for you.