Here the steps:
1) Backup the following directories on the old server: /var/www, /var/vmail and /etc, ensure that you preserve permissions e.g. with "tar pczf backupfile.tar.gz /directory/to/backup".
2) backup all mysql databases.
3) install ispconfig on the new server.
4) backup the new dbispconfig database and empty the database afterwards. Then restore the database of the old server.
5) copy all users and groups of the websites (users are web1, web2, ... , groups are client1, client2, ..., etc.) from the files /etc/passwd, /etc/shadow, /etc/group and /etc/gshadow from the old server to the new server. Copy only the lines of the users and groups, not the whole files! and make a backup of the files before you change them.
6) restore the contents of /var/vmail and /var/www on the new server.
7) restore the databases of the clients
8) Login to ispconfig, go to tools > resync, check all checkboxes and click on start and wait a few minutes to let ispconfig write missing config files.